What separates a vector quantity from a scalar quantity?

A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.

When is the point-object model useful in kinematics?

When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.

When may the constant-acceleration kinematic equations be used?

Only over an interval with constant acceleration. They are not general formulas for changing acceleration.

Why must a velocity statement name or imply a reference frame?

Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.

Why can horizontal and vertical projectile motion be analyzed separately?

Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.

Can an object have zero velocity and nonzero acceleration at one instant?

Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.

A runner completes one lap and returns to the start. How do distance and displacement compare?

The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.

What makes a reference frame convenient for a motion problem?

It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.

How are the components of a launch velocity v at angle θ found?

v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.

What does average velocity measure?

Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.

Do a vector's magnitude and its component use different SI units?

No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.

A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?

The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.

What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?

a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.

What does average acceleration measure?

Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.

What does a negative one-dimensional vector component mean?

It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.

For constant acceleration, what does v = v₀ + at retrieve?

Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.

How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?

v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.

At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?

It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.

What does the slope of a position-versus-time graph represent?

Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.

Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?

Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.

A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?

They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.

A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?

+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².

If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?

The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.

For constant acceleration, what does Δx = v₀t + ½at² retrieve?

Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.

For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?

The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.

Why can average speed differ from the magnitude of average velocity?

Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.

What does the slope of a velocity-versus-time graph represent?

Acceleration. The slope's units are (m/s)/s = m/s².

A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?

20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.

Does projectile mass affect the ideal trajectory when air resistance is negligible?

No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.

Can an object have nonzero velocity and zero acceleration?

Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.

A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?

Position x versus t². Its slope is ½a when the initial velocity is zero.

What does signed area under a velocity-versus-time graph represent?

Displacement. Area below the time axis contributes negative displacement.

At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?

v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.

How can a motion sensor test whether a cart moves at constant velocity?

Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.

A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?

-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.

Which constant-acceleration equation connects speed and displacement without using time?

v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.

How could video data test the independence of projectile components?

Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.

A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?

The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.

How can average velocity over a very short interval approximate instantaneous velocity?

Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.

A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?

+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.

What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?

A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.

In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?

Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.

What does signed area under an acceleration-versus-time graph represent?

Change in velocity. Add that signed area to the initial velocity to find the final velocity.

How is one-dimensional relative velocity calculated for two objects A and B?

v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.

When its speed is nonzero, what direction does a projectile's instantaneous velocity point?

Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.

What does choosing a system boundary decide in a mechanics problem?

It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.

What belongs on a free-body diagram for one chosen object?

Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.

What assumptions define the ideal-string model used in introductory algebra-based physics?

The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.

What does translational equilibrium require?

Zero net force. The object may be at rest or move with constant velocity.

In an inertial frame, how does Newton's second law connect force and motion?

ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.

How do mass and weight differ?

Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.

Algebra-Based Physics 1 Flashcards: Complete 8-Unit Course Review

A 400-card review of concepts, formulas, graphs, experiments, and reasoning across eight units of algebra-based physics.

Автор Flashcards Open Source App

Об этой колоде

This 400-card deck reviews concepts, formulas, graphs, experiments, and reasoning across eight units of algebra-based physics. It moves through Kinematics; Force and Translational Dynamics; Work, Energy, and Power; Linear Momentum; Torque and Rotational Dynamics; Energy and Momentum of Rotating Systems; Oscillations; and Fluids.

What you'll retrieve

Choose the governing principle for a situation or claim, then explain the prediction in plain language.
Recall what a quantity or equation means, when it applies, how it scales, and which SI unit it uses.
Read slopes, signed areas, extrema, signs, and shapes across motion, force, energy, momentum, rotation, oscillation, and fluid graphs.
Plan a small experiment by naming useful variables, measurements, controls, linearized graphs, slope meanings, and uncertainty checks.
Solve one focused original algebra-based setup with units and a short reason.
Use selected reverse and contrast prompts to recognize conditions and separate common confusion pairs. The deck doesn't mechanically reverse every fact.

Bare formula-to-symbol lists, long multipart calculations, and imitation exam questions are excluded. The deck also stays outside calculus-based mechanics, three-dimensional angular-momentum analysis, electricity and magnetism, circuits, thermodynamics, waves and optics, modern physics, viscous-flow effects and nonideal viscosity corrections, turbulence, surface tension, and other topics beyond this algebra-based scope.

The order is deliberate: Units 1–4 establish motion, forces, energy, and momentum; Units 5–6 reuse those ideas for rotation and orbits; Unit 7 applies them to oscillations; Unit 8 closes with static and moving ideal fluids. Its release-direction cards ask only for the immediate acceleration in a static, uniform ideal fluid when weight and buoyancy are the only forces. Definitions appear before dependent uses. The sequence interleaves closely related formula, graph, condition, calculation, and contrast prompts with unrelated retrievals. Short prerequisite steps stay closer only when each card introduces a genuinely different idea.

Every prompt, answer, numerical setup, explanation, ordering choice, and metadata field was independently written from common physics knowledge and checked with compatible or authoritative fact sources. The CC0 label applies to that original expression and organization to the extent applicable rights exist; it does not claim ownership of common physics facts or third-party material.

This is an independently authored, unofficial educational deck by Flashcards Open Source App. It is not affiliated with or endorsed by any course or exam provider. No exam questions, mark schemes, curriculum prose, commercial deck text, source prose, logos, figures, or trade dress were copied.

Карточки в этой колоде

Карточка 1
Вопрос
What separates a vector quantity from a scalar quantity?
Ответ
A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.
Карточка 2
Вопрос
When is the point-object model useful in kinematics?
Ответ
When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.
Карточка 3
Вопрос
When may the constant-acceleration kinematic equations be used?
Ответ
Only over an interval with constant acceleration. They are not general formulas for changing acceleration.
Карточка 4
Вопрос
Why must a velocity statement name or imply a reference frame?
Ответ
Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.
Карточка 5
Вопрос
Why can horizontal and vertical projectile motion be analyzed separately?
Ответ
Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.
Карточка 6
Вопрос
Can an object have zero velocity and nonzero acceleration at one instant?
Ответ
Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.
Карточка 7
Вопрос
A runner completes one lap and returns to the start. How do distance and displacement compare?
Ответ
The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.
Карточка 8
Вопрос
What makes a reference frame convenient for a motion problem?
Ответ
It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.
Карточка 9
Вопрос
How are the components of a launch velocity v at angle θ found?
Ответ
v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.
Карточка 10
Вопрос
What does average velocity measure?
Ответ
Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.
Карточка 11
Вопрос
Do a vector's magnitude and its component use different SI units?
Ответ
No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.
Карточка 12
Вопрос
A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?
Ответ
The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.
Карточка 13
Вопрос
What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?
Ответ
a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.
Карточка 14
Вопрос
What does average acceleration measure?
Ответ
Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.
Карточка 15
Вопрос
What does a negative one-dimensional vector component mean?
Ответ
It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.
Карточка 16
Вопрос
For constant acceleration, what does v = v₀ + at retrieve?
Ответ
Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.
Карточка 17
Вопрос
How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?
Ответ
v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.
Карточка 18
Вопрос
At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?
Ответ
It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.
Карточка 19
Вопрос
What does the slope of a position-versus-time graph represent?
Ответ
Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.
Карточка 20
Вопрос
Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?
Ответ
Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.
Карточка 21
Вопрос
A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?
Ответ
They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.
Карточка 22
Вопрос
A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?
Ответ
+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².
Карточка 23
Вопрос
If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?
Ответ
The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.
Карточка 24
Вопрос
For constant acceleration, what does Δx = v₀t + ½at² retrieve?
Ответ
Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.
Карточка 25
Вопрос
For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?
Ответ
The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.
Карточка 26
Вопрос
Why can average speed differ from the magnitude of average velocity?
Ответ
Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.
Карточка 27
Вопрос
What does the slope of a velocity-versus-time graph represent?
Ответ
Acceleration. The slope's units are (m/s)/s = m/s².
Карточка 28
Вопрос
A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?
Ответ
20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.
Карточка 29
Вопрос
Does projectile mass affect the ideal trajectory when air resistance is negligible?
Ответ
No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.
Карточка 30
Вопрос
Can an object have nonzero velocity and zero acceleration?
Ответ
Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.
Карточка 31
Вопрос
A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?
Ответ
Position x versus t². Its slope is ½a when the initial velocity is zero.
Карточка 32
Вопрос
What does signed area under a velocity-versus-time graph represent?
Ответ
Displacement. Area below the time axis contributes negative displacement.
Карточка 33
Вопрос
At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?
Ответ
v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.
Карточка 34
Вопрос
How can a motion sensor test whether a cart moves at constant velocity?
Ответ
Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.
Карточка 35
Вопрос
A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?
Ответ
-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.
Карточка 36
Вопрос
Which constant-acceleration equation connects speed and displacement without using time?
Ответ
v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.
Карточка 37
Вопрос
How could video data test the independence of projectile components?
Ответ
Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.
Карточка 38
Вопрос
A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?
Ответ
The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.
Карточка 39
Вопрос
How can average velocity over a very short interval approximate instantaneous velocity?
Ответ
Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.
Карточка 40
Вопрос
A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?
Ответ
+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.
Карточка 41
Вопрос
What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?
Ответ
A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.
Карточка 42
Вопрос
In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?
Ответ
Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.
Карточка 43
Вопрос
What does signed area under an acceleration-versus-time graph represent?
Ответ
Change in velocity. Add that signed area to the initial velocity to find the final velocity.
Карточка 44
Вопрос
How is one-dimensional relative velocity calculated for two objects A and B?
Ответ
v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.
Карточка 45
Вопрос
When its speed is nonzero, what direction does a projectile's instantaneous velocity point?
Ответ
Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.
Карточка 46
Вопрос
What does choosing a system boundary decide in a mechanics problem?
Ответ
It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.
Карточка 47
Вопрос
What belongs on a free-body diagram for one chosen object?
Ответ
Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.
Карточка 48
Вопрос
What assumptions define the ideal-string model used in introductory algebra-based physics?
Ответ
The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.
Карточка 49
Вопрос
What does translational equilibrium require?
Ответ
Zero net force. The object may be at rest or move with constant velocity.
Карточка 50
Вопрос
In an inertial frame, how does Newton's second law connect force and motion?
Ответ
ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.
Карточка 51
Вопрос
How do mass and weight differ?
Ответ
Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.
Карточка 52
Вопрос
How does static friction choose its magnitude before slipping begins?
Ответ
It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.
Карточка 53
Вопрос
For an ideal spring in its linear range, what is the spring force when its end is displaced by a signed amount x from the relaxed or natural length?
Ответ
F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.
Карточка 54
Вопрос
What direction does centripetal acceleration point in circular motion?
Ответ
Toward the circle's center. It changes the velocity's direction even when speed is constant.
Карточка 55
Вопрос
What is the gravitational force magnitude between two point masses?
Ответ
F_g = Gm₁m₂/r². Here r is the center-to-center separation.
Карточка 56
Вопрос
Why isn't the normal force always equal to an object's weight?
Ответ
It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.
Карточка 57
Вопрос
What determines a friction coefficient in the simple model?
Ответ
The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.
Карточка 58
Вопрос
What is the centripetal-acceleration magnitude for speed v and radius r?
Ответ
a_c = v²/r. It is a kinematic requirement, not a separate force.
Карточка 59
Вопрос
An elevator accelerates upward. How does the scale reading compare with a rider's weight?
Ответ
It is greater than the weight. Upward net force requires N - mg > 0.
Карточка 60
Вопрос
What does a spring constant k measure, and what is its SI unit?
Ответ
It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.
Карточка 61
Вопрос
Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?
Ответ
At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.
Карточка 62
Вопрос
What provides centripetal force?
Ответ
The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.
Карточка 63
Вопрос
How is near-surface gravitational field strength related to weight?
Ответ
F_g = mg. The local field strength g has units N/kg, equivalent to m/s².
Карточка 64
Вопрос
How is weight resolved on an incline of angle θ measured from horizontal?
Ответ
mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.
Карточка 65
Вопрос
What does Newton's third law say about an interaction between objects A and B?
Ответ
The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.
Карточка 66
Вопрос
What does signed tangential acceleration describe during circular motion?
Ответ
It describes how quickly speed changes and which way the tangential acceleration points along the chosen tangent. Its magnitude is the absolute value of the instantaneous rate of change of speed. If it points with the velocity, speed increases; if it points against the velocity, speed decreases. Its sign follows the chosen tangent.
Карточка 67
Вопрос
What happens to gravitational force if the separation between two point masses doubles?
Ответ
It becomes one-fourth as large. The force follows an inverse-square dependence on distance.
Карточка 68
Вопрос
How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?
Ответ
Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.
Карточка 69
Вопрос
In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?
Ответ
The net external force divided by the system's total mass. Internal force pairs cannot change the center-of-mass motion of the whole system.
Карточка 70
Вопрос
Which tension components act for a conical pendulum?
Ответ
The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.
Карточка 71
Вопрос
What does apparent weight measure for an object supported by one surface?
Ответ
The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.
Карточка 72
Вопрос
How are several forces combined to find net force?
Ответ
Add them as vectors, component by component. Opposing components subtract according to the chosen signs.
Карточка 73
Вопрос
Why is tension uniform along one continuous ideal string?
Ответ
Every massless segment must have zero net force in the ideal model. Without frictional contact or a massive pulley changing it, the tension magnitude stays the same throughout the string.
Карточка 74
Вопрос
A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?
Ответ
4 N. F_in = mv²/r = 0.5 × 16 / 2.
Карточка 75
Вопрос
What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?
Ответ
A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.
Карточка 76
Вопрос
For the same net force, what happens to acceleration if mass doubles?
Ответ
Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.
Карточка 77
Вопрос
How do static and kinetic friction coefficients usually compare for the same pair of surfaces?
Ответ
Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.
Карточка 78
Вопрос
How are radial and tangential acceleration combined when circular speed changes?
Ответ
Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).
Карточка 79
Вопрос
A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?
Ответ
It is twice as large. Surface field strength follows g = GM/R².
Карточка 80
Вопрос
Does a force have to point in the direction of motion?
Ответ
No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.
Карточка 81
Вопрос
Where is the center of mass of a uniform object with a symmetric mass distribution?
Ответ
At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.
Карточка 82
Вопрос
How are speed, period, and frequency related in uniform circular motion?
Ответ
v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.
Карточка 83
Вопрос
Why is an object apparently weightless in free fall?
Ответ
Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.
Карточка 84
Вопрос
Can forces balance along one axis while an object accelerates along another?
Ответ
Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.
Карточка 85
Вопрос
Why don't Newton's third-law forces cancel on one object's free-body diagram?
Ответ
Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.
Карточка 86
Вопрос
On a frictionless banked curve, which force components create vertical balance and inward acceleration?
Ответ
The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.
Карточка 87
Вопрос
What motion results when the net force on an object is zero in an inertial frame?
Ответ
Constant velocity. Rest is the special case with constant velocity equal to zero.
Карточка 88
Вопрос
A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?
Ответ
4 m/s². Use a = ΣF/m = 12/3.
Карточка 89
Вопрос
What does the observed equivalence of inertial and gravitational mass imply for free fall?
Ответ
Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.
Карточка 90
Вопрос
Does friction in the simple dry-friction model depend on apparent contact area?
Ответ
No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.
Карточка 91
Вопрос
When should Hooke's-law predictions be treated cautiously?
Ответ
When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.
Карточка 92
Вопрос
What bank angle θ supports speed v on an ideal frictionless curve of radius r?
Ответ
tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.
Карточка 93
Вопрос
Why do internal forces cancel when finding the net force on a complete system?
Ответ
They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.
Карточка 94
Вопрос
An elevator moves downward at constant speed. How does the scale reading compare with weight?
Ответ
It equals the weight. Constant velocity means zero acceleration and N - mg = 0.
Карточка 95
Вопрос
What assumptions let an ideal pulley redirect a string without changing its tension magnitude?
Ответ
The pulley is massless and frictionless, and the string is ideal. It changes the tension's direction while the magnitude stays the same on both sides.
Карточка 96
Вопрос
What does inertia describe?
Ответ
An object's resistance to changes in velocity. Mass measures translational inertia.
Карточка 97
Вопрос
For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?
Ответ
Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.
Карточка 98
Вопрос
Does zero net force mean no forces act?
Ответ
No. Several forces can act and cancel vectorially.
Карточка 99
Вопрос
What is the common model for kinetic-friction magnitude?
Ответ
f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.
Карточка 100
Вопрос
How could hanging masses measure the spring constant of one ideal spring?
Ответ
At static equilibrium, record the spring's extension for several known weights and graph mg versus extension. Keep the same spring in its linear range; the slope is k.
Карточка 101
Вопрос
For the same object at the same circular radius, how does required inward net force change if speed doubles?
Ответ
It becomes four times as large. F_in = mv²/r depends on speed squared.
Карточка 102
Вопрос
Where is the center of mass of two point masses on an x-axis?
Ответ
At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.
Карточка 103
Вопрос
Why must net force, rather than one selected force, be used in ΣF = ma?
Ответ
All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.
Карточка 104
Вопрос
Why can tension vary along a hanging chain with nonnegligible mass?
Ответ
Higher sections must support and accelerate more chain below them. Newton's third law still applies locally to each interaction; it does not make tension uniform everywhere.
Карточка 105
Вопрос
What makes a reference frame inertial?
Ответ
An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.
Карточка 106
Вопрос
How could carts test the proportionality between acceleration and net force?
Ответ
Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.
Карточка 107
Вопрос
How does Kepler's third-law scaling compare two satellites in circular orbits at center-to-center radii r when their masses are negligible relative to the same fixed central mass?
Ответ
T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.
Карточка 108
Вопрос
Which direction does kinetic friction act?
Ответ
Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.
Карточка 109
Вопрос
What does the slope of a spring-force-versus-displacement graph give?
Ответ
-k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.
Карточка 110
Вопрос
What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?
Ответ
v_min = √(gr). At the threshold, the support force or tension is zero.
Карточка 111
Вопрос
What is translational kinetic energy?
Ответ
Energy associated with an object's translational motion. For a point-like object, K = ½mv².
Карточка 112
Вопрос
How is work by a constant force calculated when its point of application undergoes a straight displacement?
Ответ
W = Fd cos θ. Here d is the displacement of the force's point of application, and θ is the angle between the force and that displacement.
Карточка 113
Вопрос
What does power measure?
Ответ
The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.
Карточка 114
Вопрос
What does conservation of energy say for an isolated system?
Ответ
The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.
Карточка 115
Вопрос
Can translational kinetic energy be negative?
Ответ
No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.
Карточка 116
Вопрос
What does negative work by a force mean?
Ответ
The force makes a negative contribution to the system's kinetic-energy change. Its component opposes the displacement of its point of application; potential energy may rise while total mechanical energy stays constant.
Карточка 117
Вопрос
What is the near-surface change in gravitational potential energy?
Ответ
ΔU_g = mgΔy. It applies when g can be treated as constant.
Карточка 118
Вопрос
When is a chosen system's mechanical energy K + U conserved?
Ответ
When no net energy crosses the system boundary and no internal process converts energy in either direction between mechanical and nonmechanical forms. If either condition fails, K + U can change even though total energy still balances for the system plus surroundings.
Карточка 119
Вопрос
What is the SI unit of power?
Ответ
The watt, W. One watt equals one joule per second.
Карточка 120
Вопрос
For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?
Ответ
The work–energy theorem: W_net = ΔK. Under the particle model, positive net work raises translational kinetic energy and negative net work lowers it. A rotating rigid system requires total kinetic energy and work at the forces' points of application.
Карточка 121
Вопрос
A ball falls from rest through height h near a planet's surface. For the ball–planet system, g is constant and air resistance is negligible. What speed does energy conservation predict?
Ответ
v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².
Карточка 122
Вопрос
Does choosing a different zero level for potential energy change physical predictions?
Ответ
No. Only potential-energy differences enter measurable energy changes.
Карточка 123
Вопрос
Can an engine do the same work with different average power?
Ответ
Yes. Doing the same work in less time requires greater average power.
Карточка 124
Вопрос
When does a constant nonzero force do zero work over an interval?
Ответ
When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.
Карточка 125
Вопрос
A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?
Ответ
No. With only gravity doing work, the potential-energy change depends on height, not path.
Карточка 126
Вопрос
How does translational kinetic energy change if speed doubles at constant mass?
Ответ
It becomes four times as large. Kinetic energy depends on v².
Карточка 127
Вопрос
What is the elastic potential energy of an ideal spring displaced by a signed amount x from its relaxed or natural length, with U_s = 0 there?
Ответ
U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.
Карточка 128
Вопрос
What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?
Ответ
Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.
Карточка 129
Вопрос
A chosen system starts with 20 J of mechanical energy and converts 6 J of it into thermal energy, with no energy crossing the boundary. How much mechanical energy remains?
Ответ
14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.
Карточка 130
Вопрос
What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?
Ответ
The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.
Карточка 131
Вопрос
A machine transfers 600 J in 3 s. What is its average power?
Ответ
200 W. Divide energy transferred by elapsed time.
Карточка 132
Вопрос
Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?
Ответ
The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.
Карточка 133
Вопрос
A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?
Ответ
At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.
Карточка 134
Вопрос
Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?
Ответ
They are equal. Kinetic energy uses speed and has no direction.
Карточка 135
Вопрос
What makes work by a conservative force path independent?
Ответ
It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.
Карточка 136
Вопрос
A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?
Ответ
30 J. Here θ = 0, so W = Fd = 10×3.
Карточка 137
Вопрос
How is total potential energy built for a system with several interacting pairs?
Ответ
Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.
Карточка 138
Вопрос
How should external work appear in an energy equation?
Ответ
As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.
Карточка 139
Вопрос
How does a spring launch problem combine energy forms?
Ответ
Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.
Карточка 140
Вопрос
For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?
Ответ
P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.
Карточка 141
Вопрос
How does translational kinetic energy change if mass triples at constant speed?
Ответ
It triples. Kinetic energy is directly proportional to mass.
Карточка 142
Вопрос
How much net work does a conservative force do around a path that returns to the initial configuration?
Ответ
Zero. The initial and final potential energies are the same.
Карточка 143
Вопрос
Where is stable equilibrium on a potential-energy-versus-position graph?
Ответ
At a local minimum. Small displacements produce forces that point back toward the minimum.
Карточка 144
Вопрос
Which displacement belongs in the work done by a force on a rigid object?
Ответ
The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.
Карточка 145
Вопрос
What happens to mechanical energy when kinetic friction acts inside the chosen system?
Ответ
Some mechanical energy becomes thermal energy. The broader system's total energy still balances.
Карточка 146
Вопрос
A nonrotating particle falls from rest through vertical drop h under constant g. If its gravitational-potential decrease becomes only translational kinetic energy, with no other energy changes, what graph linearizes final speed?
Ответ
Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.
Карточка 147
Вопрос
If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?
Ответ
Measure each student's mass, vertical rise, and climb time, then calculate mgh/t. Equal initial and final speeds make ΔK = 0; if ΔK is negligible, the result is an approximation. This is mechanical output power against gravity, not metabolic input power.
Карточка 148
Вопрос
How can force-sensor data measure work when force changes as its point of application moves?
Ответ
Graph the force component along the motion against the point-of-application position and find the signed area. A rectangle formula isn't enough for a varying force.
Карточка 149
Вопрос
Why is potential energy assigned to a system rather than one isolated object?
Ответ
It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.
Карточка 150
Вопрос
How can work by a nonconservative force depend on path?
Ответ
Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.
Карточка 151
Вопрос
A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?
Ответ
9 J. K = ½(2)(3²) = 9 J.
Карточка 152
Вопрос
A block slides distance d across a stationary surface while constant kinetic friction f_k opposes its displacement. What work does friction do on the block?
Ответ
W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.
Карточка 153
Вопрос
A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?
Ответ
+100 J. ΔU_g = mgΔy = 2 × 10 × 5.
Карточка 154
Вопрос
Why are energy bar charts useful?
Ответ
They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.
Карточка 155
Вопрос
A motor lifts the same load through the same height twice as fast. Both lifts begin and end at the same speeds and have equal or negligible dissipative losses. How do the motor's mechanical output work and average power compare?
Ответ
The mechanical output work is unchanged, while average power doubles. The two lifts have the same ΔU_g, the same ΔK, and the same losses, so the same output energy is delivered in half the time.
Карточка 156
Вопрос
A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?
Ответ
6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².
Карточка 157
Вопрос
Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?
Ответ
Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.
Карточка 158
Вопрос
What does a steep potential-energy graph imply about force magnitude in one dimension?
Ответ
A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).
Карточка 159
Вопрос
An ideal spring with k = 80 N/m is compressed 0.50 m from its relaxed length. With U_s = 0 at that length, what elastic energy is stored?
Ответ
10 J. U_s = ½(80)(0.50²).
Карточка 160
Вопрос
A constant 50 N force acts while its point of application moves at 4 m/s in the force direction. What mechanical power is delivered?
Ответ
200 W. P = Fv_point = 50 × 4.
Карточка 161
Вопрос
If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?
Ответ
They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.
Карточка 162
Вопрос
Does an object's translational kinetic energy depend on the reference frame?
Ответ
Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.
Карточка 163
Вопрос
Why can work depend on the system boundary?
Ответ
Changing the system can reclassify energy transfer. For example, friction may be external work on one system but internal thermal-energy conversion in a larger system.
Карточка 164
Вопрос
A force-component-versus-position graph for the force's point of application forms a triangle of base 4 m and height 6 N above the axis. What work does it show?
Ответ
12 J. The signed area is ½×4×6.
Карточка 165
Вопрос
A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?
Ответ
+38 J. Add the signed transfers across the boundary: 50 J - 12 J.
Карточка 166
Вопрос
What is the clearest first step in an energy-conservation problem?
Ответ
Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.
Карточка 167
Вопрос
Why can energy methods solve some problems without finding time?
Ответ
Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.
Карточка 168
Вопрос
Why can a force's instantaneous mechanical power be zero while the force is nonzero?
Ответ
Its point of application may be instantaneously at rest, or the force may be perpendicular to that point's velocity. In either case F·v_point = 0.
Карточка 169
Вопрос
What is the SI unit of kinetic energy?
Ответ
The joule, J. One joule equals 1 kg·m²/s².
Карточка 170
Вопрос
How is work by a conservative force related to potential-energy change?
Ответ
W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.
Карточка 171
Вопрос
Where is unstable equilibrium on a potential-energy-versus-position graph?
Ответ
At a local maximum. A small displacement produces a force that pushes the system farther away.
Карточка 172
Вопрос
For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?
Ответ
No. The inward net force is perpendicular to the particle's instantaneous velocity, so its net work is zero and it changes the velocity's direction rather than its magnitude.
Карточка 173
Вопрос
Why should thermal energy not be written as a force?
Ответ
Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.
Карточка 174
Вопрос
How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?
Ответ
Measure speed and height at several points, calculate K + U_g with one consistent zero level, and compare within uncertainty. Systematic drift suggests unmodeled energy transfer or conversion.
Карточка 175
Вопрос
According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?
Ответ
Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.
Карточка 176
Вопрос
What is linear momentum?
Ответ
p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.
Карточка 177
Вопрос
How is a multi-object system's total momentum found?
Ответ
Add every object's momentum as a vector. In one dimension, add signed values.
Карточка 178
Вопрос
For a chosen object or system, what is external impulse?
Ответ
The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.
Карточка 179
Вопрос
What experimental uncertainty matters strongly when comparing collision kinetic energies?
Ответ
Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.
Карточка 180
Вопрос
Why can two objects bounce apart yet still collide inelastically?
Ответ
Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Карточка 181
Вопрос
A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?
Ответ
+12 kg·m/s. p = mv = 3 × 4.
Карточка 182
Вопрос
Why can momentum be negative while kinetic energy cannot?
Ответ
Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.
Карточка 183
Вопрос
When is a system's total linear momentum conserved?
Ответ
When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.
Карточка 184
Вопрос
Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?
Ответ
They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.
Карточка 185
Вопрос
Can total kinetic energy increase in an explosion?
Ответ
Yes. Stored internal energy can become kinetic energy. Total momentum is conserved for a defined system with zero or negligible net external impulse, while total energy remains conserved for the system plus surroundings.
Карточка 186
Вопрос
How is total momentum related to center-of-mass velocity?
Ответ
p_total = Mv_cm. M is the system's total mass.
Карточка 187
Вопрос
How does a nonzero external impulse affect system momentum?
Ответ
It changes total momentum by that impulse. J_external = Δp_system.
Карточка 188
Вопрос
Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?
Ответ
They are equal in magnitude and opposite in direction. The system began with zero total momentum.
Карточка 189
Вопрос
What are equivalent SI units for impulse?
Ответ
N·s and kg·m/s. Both represent a change in momentum.
Карточка 190
Вопрос
What defines an elastic collision?
Ответ
Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.
Карточка 191
Вопрос
How can a force sensor and motion detector test the impulse–momentum theorem for one cart?
Ответ
Account for every external force component along the measured axis, compare the net-force–time area with m(v_f - v_i), and include uncertainty. Agreement supports J_external = Δp.
Карточка 192
Вопрос
A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?
Ответ
Left. The person and boat acquire opposite momenta so total momentum remains zero.
Карточка 193
Вопрос
Why must momentum signs be kept through an impulse calculation?
Ответ
Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.
Карточка 194
Вопрос
What defines a perfectly inelastic collision?
Ответ
The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.
Карточка 195
Вопрос
Why can momentum be conserved during a collision even when large forces act?
Ответ
For a defined system with zero or negligible net external impulse, the large collision forces are internal. Their equal-and-opposite impulses cancel within that system.
Карточка 196
Вопрос
Two objects have equal speed. Which has the larger momentum magnitude?
Ответ
The object with larger mass. At equal speed, momentum is proportional to mass.
Карточка 197
Вопрос
How is momentum conservation written for a two-dimensional isolated interaction?
Ответ
Conserve components separately: Σp_x,i = Σp_x,f and Σp_y,i = Σp_y,f. Both component equations must hold for the same interaction.
Карточка 198
Вопрос
For a chosen object or system, how is average net external force related to impulse?
Ответ
F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.
Карточка 199
Вопрос
Which conservation law alone can determine the shared final velocity of a sticking collision?
Ответ
Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.
Карточка 200
Вопрос
Two equal momentum vectors point along +x and +y. What direction does their total momentum point?
Ответ
At 45° between the positive axes. Equal perpendicular components produce that resultant direction.
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Карточка 201
Вопрос
If external impulse during a collision is small but not zero, what should experimental data show?
Ответ
Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.
Карточка 202
Вопрос
A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?
Ответ
It does not change. Impulse depends on total signed area, not peak force alone.
Карточка 203
Вопрос
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, how does final kinetic energy compare with the initial 8 J?
Ответ
It is 4 J, half the initial value. The 4 J decrease in translational kinetic energy becomes internal or thermal energy through deformation, and some energy may be carried by sound.
Карточка 204
Вопрос
How can a nearly frictionless cart track improve a momentum-conservation test?
Ответ
It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.
Карточка 205
Вопрос
How does an object's momentum change if its speed doubles at constant mass?
Ответ
Its momentum magnitude doubles. Momentum depends linearly on speed.
Карточка 206
Вопрос
For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?
Ответ
External impulse, which equals the change in that object's or system's momentum. Area below the time axis contributes negative impulse under the graph's sign convention.
Карточка 207
Вопрос
A firework at rest explodes into two pieces with negligible external impulse. If one piece has twice the mass, how do the piece speeds compare?
Ответ
The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.
Карточка 208
Вопрос
Why is sticking evidence of an inelastic collision?
Ответ
The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.
Карточка 209
Вопрос
Can a moving two-object system have zero total momentum?
Ответ
Yes. Equal and opposite momenta cancel even though each object is moving.
Карточка 210
Вопрос
A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?
Ответ
3 N·s in the force direction. Multiply the net external force by the interaction time.
Карточка 211
Вопрос
What does a momentum-versus-velocity graph's slope represent for one object?
Ответ
Its mass. The relationship p = mv is linear through the origin.
Карточка 212
Вопрос
A 2 kg cart at +3 m/s sticks to a 1 kg cart at rest. If external horizontal impulse is negligible, what is their final velocity?
Ответ
+2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).
Карточка 213
Вопрос
An isolated two-dimensional interaction has known initial total momentum p_total,i and known first outgoing momentum p₁,f. How is the second outgoing momentum found?
Ответ
Subtract component by component: p₂,f = p_total,i - p₁,f. Thus p₂x,f = p_total,x,i - p₁x,f, with the same subtraction for y.
Карточка 214
Вопрос
A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?
Ответ
-8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).
Карточка 215
Вопрос
What remains conserved in an isolated inelastic collision?
Ответ
Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Карточка 216
Вопрос
Why does choosing both colliding objects as the system simplify momentum analysis?
Ответ
Their contact forces become internal. Only external impulse can change the system total.
Карточка 217
Вопрос
For a chosen object or system, what does the slope of its momentum-versus-time graph represent?
Ответ
Net external force. A steeper slope means a larger force in the slope's signed direction.
Карточка 218
Вопрос
Why do airbags reduce injury force during a stop?
Ответ
They increase the stopping time for roughly the same momentum change. That lowers the average force.
Карточка 219
Вопрос
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, what final speed do they share?
Ответ
2 m/s. Momentum 4 kg·m/s is shared by 2 kg.
Карточка 220
Вопрос
For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?
Ответ
First verify total momentum within uncertainty, then compare total kinetic energy. Unchanged kinetic energy supports elastic behavior; any change beyond uncertainty means the collision isn't elastic, with a decrease indicating an ordinary inelastic collision.
Карточка 221
Вопрос
What is angular displacement?
Ответ
The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.
Карточка 222
Вопрос
For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?
Ответ
Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.
Карточка 223
Вопрос
For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?
Ответ
Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.
Карточка 224
Вопрос
What does rotational inertia measure?
Ответ
Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.
Карточка 225
Вопрос
What is the lever arm in a torque calculation?
Ответ
The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.
Карточка 226
Вопрос
For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?
Ответ
ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.
Карточка 227
Вопрос
Two points lie on the same rotating rigid disk. Which rotational quantities are the same?
Ответ
They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.
Карточка 228
Вопрос
How is rotational inertia found for a collection of point masses?
Ответ
I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.
Карточка 229
Вопрос
What determines the magnitude of torque from one force about a chosen axis?
Ответ
τ = rF sin θ = r_perp F. The radius vector r runs from the axis to the force's point of application, θ is the angle between r and the force, and r_perp is the lever arm.
Карточка 230
Вопрос
What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?
Ответ
Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.
Карточка 231
Вопрос
For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?
Ответ
Δs = rΔθ. Here r is the point's perpendicular distance from the fixed axis, and both displacements use matching sign conventions along the circular path.
Карточка 232
Вопрос
In a planar rigid-body model, can an object with zero net external force and zero net external torque about its center of mass be moving?
Ответ
Yes. Its center of mass may translate at constant velocity while it rotates at constant angular velocity; the stated zero net force and center-of-mass torque don't require rest.
Карточка 233
Вопрос
At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?
Ответ
Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.
Карточка 234
Вопрос
How are clockwise and counterclockwise torques combined?
Ответ
Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.
Карточка 235
Вопрос
For the same rigid system with constant rotational inertia about the same axis fixed in an inertial frame, what happens if net-external-torque magnitude doubles?
Ответ
Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.
Карточка 236
Вопрос
Why must an axis be named when stating rotational inertia?
Ответ
The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.
Карточка 237
Вопрос
For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?
Ответ
Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.
Карточка 238
Вопрос
Why is torque's unit N·m not called a joule?
Ответ
Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.
Карточка 239
Вопрос
A rigid wheel has constant I = 2 kg·m² about an axis fixed in an inertial frame and net external torque 8 N·m about that axis. What is its angular-acceleration magnitude?
Ответ
4 rad/s². |α| = |Στ_external|/I = 8/2.
Карточка 240
Вопрос
Where can the weight of a rigid object be treated as acting in a uniform gravitational field?
Ответ
At the object's center of mass. That single force gives the same net gravitational force and torque.
Карточка 241
Вопрос
For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?
Ответ
v_t = r|ω|. Here r is the perpendicular distance from the fixed axis. Points farther from the axis move faster even though the rigid body has one angular velocity.
Карточка 242
Вопрос
For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?
Ответ
Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.
Карточка 243
Вопрос
A free-body diagram for a rigid bar must support a torque calculation about a marked axis. What must it show besides each force's direction and magnitude?
Ответ
Each force's point of application or line of action relative to the axis. That geometry sets the lever arm and torque sign; omitting it can preserve the net-force picture while losing the net torque.
Карточка 244
Вопрос
For the same rigid system about the same axis fixed in an inertial frame, what does the slope of a net-external-torque-versus-angular-acceleration graph represent?
Ответ
Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.
Карточка 245
Вопрос
A thin hoop and solid disk have the same mass and radius and rotate about their central symmetry axes. With I_hoop = MR² and I_disk = ½MR², which has larger I?
Ответ
The hoop. More of its mass lies far from the axis.
Карточка 246
Вопрос
Why can a rigid object have zero net external force but nonzero net external torque?
Ответ
External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.
Карточка 247
Вопрос
Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?
Ответ
ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.
Карточка 248
Вопрос
A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?
Ответ
4 N·m. τ = rF for a perpendicular force.
Карточка 249
Вопрос
For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?
Ответ
For a positive tangent consistent with the angular sign convention, a_t = rα. Its alignment or opposition with velocity determines whether speed increases or decreases.
Карточка 250
Вопрос
Why can two equal-mass rigid wheels have different angular-acceleration magnitudes under equal net-external-torque magnitudes about comparable axes fixed in an inertial frame?
Ответ
Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.
Карточка 251
Вопрос
For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?
Ответ
Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.
Карточка 252
Вопрос
A rigid object rests on a support that is slowly tilted in uniform gravity. If gravity and support contact are its only external interactions, sufficient static friction prevents slipping, and the motion is quasistatic, what marks the onset of tipping?
Ответ
The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.
Карточка 253
Вопрос
A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?
Ответ
The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.
Карточка 254
Вопрос
Does moving the chosen pivot change an individual force's torque?
Ответ
Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.
Карточка 255
Вопрос
How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?
Ответ
I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.
Карточка 256
Вопрос
How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?
Ответ
Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.
Карточка 257
Вопрос
For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?
Ответ
a_r = v_t²/r = rω². The acceleration points toward the axis. At r = 0, use a_r = rω² = 0; the quotient form isn't defined there.
Карточка 258
Вопрос
How could a meterstick experiment test torque balance?
Ответ
Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.
Карточка 259
Вопрос
For uniform rotation at frequency f, what is the angular-speed magnitude?
Ответ
|ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.
Карточка 260
Вопрос
Why is choosing the pivot at an unknown support force often useful?
Ответ
That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.
Карточка 261
Вопрос
Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?
Ответ
The parallel axis through the center of mass. Any offset adds the positive term Md².
Карточка 262
Вопрос
Compare rigid systems with constant rotational inertia about comparable axes fixed in an inertial frame. If net external torque is the same but I triples, what happens to angular acceleration?
Ответ
It becomes one-third as large. For each stated system, α = Στ_external/I.
Карточка 263
Вопрос
A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?
Ответ
3 m/s. v_t = r|ω| = 0.50 × 6.
Карточка 264
Вопрос
A 30 N child sits 2 m left of a seesaw pivot. If the seesaw's own weight acts through the pivot, where should a 20 N child sit on the right for balance?
Ответ
3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.
Карточка 265
Вопрос
For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?
Ответ
Angular displacement over elapsed time t. Use signed angular quantities about that axis; the equation combines the initial angular-velocity contribution with the change caused by constant α.
Карточка 266
Вопрос
A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?
Ответ
6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.
Карточка 267
Вопрос
How does moving mass farther from a rotation axis affect rotational inertia?
Ответ
It increases rotational inertia strongly. For a point mass, I = mr².
Карточка 268
Вопрос
How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?
Ответ
Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.
Карточка 269
Вопрос
Why must angular displacement be in radians for Δs = rΔθ?
Ответ
Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.
Карточка 270
Вопрос
When does a nonzero force produce zero torque about an axis?
Ответ
When its line of action passes through the axis. The lever arm is then zero.
Карточка 271
Вопрос
What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?
Ответ
L = Iω about that axis. Use one signed-axis convention consistently for L and ω.
Карточка 272
Вопрос
What magnitude relation holds for a planar, constant-radius rigid object whose center of mass lies on its rolling axis when it rolls without slipping on a stationary surface?
Ответ
v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.
Карточка 273
Вопрос
For a rigid system rotating about an axis fixed in an inertial frame, how is work by a constant torque about that axis related to angular displacement?
Ответ
W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.
Карточка 274
Вопрос
For point masses—or nonoverlapping spherical bodies—M and m separated center to center by r, what is gravitational potential energy with zero at infinity?
Ответ
U_g = -GMm/r. The negative sign reflects U_g = 0 at infinity and attraction. In an isolated gravity-only inverse-square system, total mechanical energy determines binding: E < 0 is bound, while E ≥ 0 is unbound.
Карточка 275
Вопрос
When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?
Ответ
When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.
Карточка 276
Вопрос
What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?
Ответ
It converts mechanical energy into internal or thermal energy while the surfaces slide. Use qualitative energy accounting here; no no-slip relation connects the magnitudes v_cm and R|ω| during the slip.
Карточка 277
Вопрос
What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?
Ответ
L = mvr sin θ = r_perp mv. Here r points from the chosen point to the object, v is its speed, and θ is the angle between them. The SI unit is kg·m²/s.
Карточка 278
Вопрос
For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?
Ответ
Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.
Карточка 279
Вопрос
What is a rigid body's rotational kinetic energy about a fixed axis?
Ответ
K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.
Карточка 280
Вопрос
Two planar rigid objects with constant rolling radii and centers of mass on their rolling axes are released from rest on the same fixed incline. Each rolls without slipping under gravity and its contact forces, with no other applied force or torque and negligible dissipation. Which accelerates faster: the one with smaller or larger I_cm/(MR²)?
Ответ
The one with smaller I_cm/(MR²). Here I_cm is rotational inertia about the center of mass, M is total mass, and R is that object's constant rolling radius. Under the stated model, a_cm = g sin θ/(1 + I_cm/(MR²)).
Карточка 281
Вопрос
How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?
Ответ
Choose the platform, rider, and moved masses as one system. In both the initial and final arrangements, wait until the rider and moved masses are stationary relative to the platform and the whole system co-rotates with one common signed angular velocity; then measure I_i, ω_i, I_f, and ω_f and compare I_iω_i with I_fω_f. Keep net external torque about the axis negligible, reduce bearing friction, and include uncertainty.
Карточка 282
Вопрос
For a satellite of mass m negligible beside a fixed central mass M, how are K, U_g, and total mechanical energy E related in a gravity-only circular orbit at center-to-center radius r?
Ответ
K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).
Карточка 283
Вопрос
For a rigid system rotating about an axis fixed in an inertial frame, how is instantaneous mechanical power delivered by a torque about that axis related to angular velocity?
Ответ
P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.
Карточка 284
Вопрос
In a planar common-axis rigid-body model, what kinetic-energy expression applies to a body rolling without slipping, with I_cm and ω taken about the same axis through its center of mass?
Ответ
K = ½Mv_cm² + ½I_cmω². In this model, the rigid body's motion combines center-of-mass translation with rotation about one axis through the center of mass. I_cm and ω must refer to that same axis.
Карточка 285
Вопрос
Does angular-momentum conservation require rotational kinetic-energy conservation?
Ответ
No. Internal work can change rotational kinetic energy while angular momentum stays constant.
Карточка 286
Вопрос
Why do astronauts feel weightless in orbit even though gravity acts on them?
Ответ
They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.
Карточка 287
Вопрос
Two wheels spin at the same angular speed. Which has more rotational kinetic energy?
Ответ
The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.
Карточка 288
Вопрос
For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?
Ответ
Net external torque on the system about that axis. A constant slope means constant signed net external torque there.
Карточка 289
Вопрос
A motor supplies 12 N·m of torque about a shaft axis fixed in the lab's inertial frame while the shaft turns in the torque direction at 10 rad/s. What mechanical power does it deliver?
Ответ
120 W. Using signed quantities about the shaft axis, P = τω = 12×10.
Карточка 290
Вопрос
While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?
Ответ
No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.
Карточка 291
Вопрос
A launched object has negligible mass relative to a fixed central mass M and starts at center-to-center radius r. What minimum speed lets it escape under gravity alone without further propulsion or drag?
Ответ
v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.
Карточка 292
Вопрос
In a planar common-axis rigid-body model, what kinetic-energy forms can a rigid body have when it translates and rotates about an axis through its center of mass?
Ответ
Both translational and rotational kinetic energy. The total is K = ½Mv_cm² + ½I_cmω², where I_cm and ω refer to the same axis through the center of mass.
Карточка 293
Вопрос
For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?
Ответ
The change in that object or system's angular momentum about the axis. For constant net external torque, ΔL = τ_net,external Δt. Use the same axis and sign convention throughout. Angular impulse has units N·m·s, equivalent to kg·m²/s.
Карточка 294
Вопрос
Two equal-mass planar rigid objects have constant rolling radii and centers of mass on their rolling axes. They start from rest at the same height and roll without slipping to the same lower endpoint with negligible dissipation. Why can their final speeds differ?
Ответ
Their rotational inertias divide the same decrease in gravitational potential energy differently between translation and rotation. A larger I_cm/(MR²) leaves less energy for translational speed, where I_cm is rotational inertia about the center of mass and R is rolling radius.
Карточка 295
Вопрос
For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?
Ответ
It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.
Карточка 296
Вопрос
How does rotational kinetic energy change if angular speed doubles at fixed I?
Ответ
It becomes four times as large. Rotational kinetic energy depends on ω².
Карточка 297
Вопрос
Why should external torque be evaluated about the same axis used for angular momentum?
Ответ
Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.
Карточка 298
Вопрос
For a chosen object or system about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-time graph represent?
Ответ
Angular impulse, equal to that object or system's ΔL about the axis. Use the graph's signed-axis convention. The area has units N·m·s, equivalent to kg·m²/s.
Карточка 299
Вопрос
Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?
Ответ
The contact point is instantaneously at rest relative to the surface, so there is no sliding. Static friction can still supply the torque needed for rolling.
Карточка 300
Вопрос
For a satellite whose mass is negligible beside a fixed central mass M, what is its speed in a gravity-only circular orbit at center-to-center radius r?
Ответ
v = √(GM/r). Gravity supplies the inward net force.
Карточка 301
Вопрос
A chosen system's included mass co-rotates with one common angular velocity before and after a change. If its rotational inertia about an axis fixed in an inertial frame doubles while net external torque about that axis is negligible, what happens to its angular speed?
Ответ
It halves. Because all included mass shares one angular velocity in each state, L = Iω applies. With the same axis and sign convention, angular-momentum conservation gives I_iω_i = I_fω_f.
Карточка 302
Вопрос
For a rigid system rotating about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-angular-position graph represent when angle is in radians?
Ответ
Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.
Карточка 303
Вопрос
Why can't the rolling condition alone prove that friction points uphill or downhill?
Ответ
Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.
Карточка 304
Вопрос
A satellite of mass m, negligible beside a fixed central mass M, follows a circular orbit at center-to-center radius r under gravity alone. What is its total mechanical energy?
Ответ
E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.
Карточка 305
Вопрос
A spinning student pulls masses closer to an axis fixed in the lab's inertial frame while net external torque about that axis is negligible. Why does angular speed increase?
Ответ
Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.
Карточка 306
Вопрос
What makes simple harmonic motion a special kind of periodic motion?
Ответ
Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.
Карточка 307
Вопрос
What does the amplitude of an SHM displacement graph represent?
Ответ
The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.
Карточка 308
Вопрос
How are period and frequency related?
Ответ
T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.
Карточка 309
Вопрос
What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?
Ответ
T = 2π√(m/k). The motion must stay in the spring's linear SHM range.
Карточка 310
Вопрос
For one-dimensional SHM, what is the equilibrium position?
Ответ
The position where the restoring force or torque—and therefore acceleration along the SHM coordinate—is zero. A stable equilibrium produces a restoring response after a small displacement.
Карточка 311
Вопрос
How far apart in phase are displacement and velocity in SHM?
Ответ
One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.
Карточка 312
Вопрос
When can a simple pendulum be modeled as SHM?
Ответ
For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.
Карточка 313
Вопрос
An oscillator completes 12 cycles in 6 s. What are its frequency and period?
Ответ
f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.
Карточка 314
Вопрос
For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?
Ответ
U_s = ½kx². It has the same value at +x and -x.
Карточка 315
Вопрос
At the equilibrium position of SHM, is the oscillator necessarily at rest?
Ответ
No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.
Карточка 316
Вопрос
How does a spring oscillator's period change if k becomes four times as large?
Ответ
The period is halved. T is proportional to 1/√k.
Карточка 317
Вопрос
How are acceleration and displacement related along the SHM coordinate?
Ответ
a = -ω²x, where ω = 2πf is the oscillation's angular frequency. Here ω describes the oscillator's phase rate, not a rigid body's rotational angular velocity. The acceleration component along the SHM coordinate points toward equilibrium.
Карточка 318
Вопрос
For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?
Ответ
E = ½kA². It stays constant when dissipative effects are negligible.
Карточка 319
Вопрос
In a small-angle pendulum, where are speed and gravitational potential energy greatest?
Ответ
Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.
Карточка 320
Вопрос
How can frequency be read from an oscillation-versus-time graph?
Ответ
Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.
Карточка 321
Вопрос
Why does an ideal mass–spring oscillator exhibit SHM?
Ответ
Its net restoring force is F_net = -kx, where x is displacement from equilibrium. The force is proportional to displacement and points back toward equilibrium.
Карточка 322
Вопрос
A horizontal ideal spring has k = 50 N/m and amplitude 0.20 m. With U_s = 0 at equilibrium, what is the oscillator's total energy?
Ответ
1 J. E = ½(50)(0.20²).
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Вопрос
At maximum positive displacement in SHM, what are velocity and acceleration?
Ответ
Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.
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Вопрос
How does a spring oscillator's period change if its mass becomes four times as large?
Ответ
The period doubles. T is proportional to √m.
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Вопрос
Why isn't uniform circular motion itself one-dimensional SHM?
Ответ
The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.
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Вопрос
For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?
Ответ
It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².
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Вопрос
In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?
Ответ
Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.
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Вопрос
Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?
Ответ
No within the ideal SHM model. The period depends on system parameters, not amplitude.
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Вопрос
How is maximum speed related to amplitude and angular frequency in SHM?
Ответ
v_max = ωA. Maximum speed occurs at equilibrium.
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Вопрос
For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?
Ответ
K = ½k(A² - x²). Subtract spring potential energy from the constant total.
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Вопрос
How far apart in phase are displacement and acceleration in SHM?
Ответ
Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.
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Вопрос
What is the period of a small-angle simple pendulum of length L when damping is negligible?
Ответ
T = 2π√(L/g). The simple-pendulum model uses a point-like bob on a light, inextensible string with a fixed support; bob mass doesn't affect the period.
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Вопрос
If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?
Ответ
It crosses equilibrium moving negative at T/4, reaches negative maximum at T/2, returns through equilibrium at 3T/4, and reaches maximum positive displacement at T.
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Вопрос
At equilibrium, how are a horizontal ideal spring oscillator's energies divided?
Ответ
Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.
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Вопрос
An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?
Ответ
Both are positive. Motion and restoring acceleration point right toward equilibrium.
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Вопрос
How does a pendulum's period change if its length becomes nine times as large?
Ответ
The period triples. T is proportional to √L.
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Вопрос
If SHM starts at maximum positive displacement, what equation gives its position?
Ответ
x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.
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Вопрос
What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?
Ответ
A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.
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Вопрос
At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?
Ответ
Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.
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Вопрос
For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?
Ответ
Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.
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Вопрос
What makes a substance a fluid?
Ответ
It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.
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Вопрос
What is mass density?
Ответ
Mass per volume: ρ = m/V. Its SI unit is kg/m³.
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Вопрос
For pressure that is uniform over a surface patch, how is it related to normal force and area?
Ответ
P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.
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Вопрос
What is volume flow rate?
Ответ
Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.
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Вопрос
What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?
Ответ
The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.
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Вопрос
What conditions support the basic Bernoulli model used here?
Ответ
Steady, incompressible, nonviscous flow along the compared flow path, with a completely filled pipe unless stated otherwise. Incompressible means a moving fluid element's density stays effectively constant. Pumps or major dissipative effects require extra terms.
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Вопрос
Under the ideal model, how does average density predict whether a free object floats or sinks?
Ответ
It floats if its average density is less than the fluid's and sinks if it is greater. Equal average density gives neutral buoyancy when fully submerged; assume no support or other external force.
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Вопрос
How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?
Ответ
Q = Av. This gives the volume crossing a completely filled pipe section per time.
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Вопрос
How does a static fluid exert force on a surface?
Ответ
Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.
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Вопрос
How does pressure change with depth in a static uniform fluid?
Ответ
It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.
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Вопрос
What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?
Ответ
F_B = mg. The object's weight equals the weight of the fluid it displaces.
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Вопрос
What is the continuity equation for steady incompressible flow in one filled pipe?
Ответ
A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.
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Вопрос
Why does a static fluid produce an upward buoyant force?
Ответ
Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.
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Вопрос
What is the absolute pressure at depth h below the open surface of a static, uniform liquid?
Ответ
P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.
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Вопрос
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density exceeds the fluid density and only weight and buoyancy act?
Ответ
Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.
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Вопрос
Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?
Ответ
0.060 m³/s. Q = Av = 0.020×3.
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Вопрос
What does the slope of a mass-versus-volume graph represent for one uniform material?
Ответ
Density. Since m = ρV, the line's slope is ρ.
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Вопрос
How do gauge pressure and absolute pressure differ?
Ответ
Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.
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Вопрос
For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?
Ответ
No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.
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Вопрос
For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?
Ответ
It doubles. Continuity keeps Av constant.
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Вопрос
When does a fluid element's velocity change?
Ответ
Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.
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Вопрос
For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?
Ответ
Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.
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Вопрос
For a uniform object floating at rest in a uniform-density fluid with buoyancy and weight as its only vertical forces, what fraction of its volume is submerged?
Ответ
V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.
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Вопрос
For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?
Ответ
It becomes four times as large. Area is proportional to radius squared.
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Вопрос
What does Pascal's principle say for a confined incompressible fluid at rest?
Ответ
An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.
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Вопрос
In a uniform static fluid, what does the slope of gauge pressure versus depth represent?
Ответ
ρg. For known g, the slope can determine fluid density.
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Вопрос
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density is less than the fluid density and only weight and buoyancy act?
Ответ
Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.
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Вопрос
For steady incompressible flow in a filled pipe, area narrows from 0.040 m² to 0.010 m². If initial speed is 2 m/s, what is final speed?
Ответ
8 m/s. Continuity gives v₂ = A₁v₁/A₂.
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Вопрос
What physical quantity does each term in P + ½ρv² + ρgy share?
Ответ
Energy per unit volume, equivalent to pressure. Every term uses units of pascals.
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Вопрос
In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?
Ответ
Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.
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Вопрос
A uniform object of density 750 kg/m³ floats at rest in uniform-density water of density 1000 kg/m³, with buoyancy and weight as its only vertical forces. What fraction is submerged?
Ответ
0.75, or 75%. Use the density ratio for floating equilibrium.
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Вопрос
A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?
Ответ
Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.
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Вопрос
For steady, incompressible, nonviscous efflux with negligible losses, what is Torricelli's speed for an opening a vertical distance h below a large open surface?
Ответ
v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.
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Вопрос
Why does the same force create more pressure on a smaller area?
Ответ
Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.
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Вопрос
A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?
Ответ
3.0×10³ kg/m³. Divide mass by volume.
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Вопрос
What conservation law underlies the continuity equation for incompressible flow?
Ответ
Conservation of mass. Constant density turns equal mass flow into equal volume flow.
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Вопрос
An immersed object rests on a scale that exerts an upward support force. If weight, buoyancy, and that support are its only vertical forces, with mg ≥ F_B, how is apparent weight related to buoyant force?
Ответ
N = mg - F_B. Here N is the upward scale-force magnitude. The fluid supports part of the object's weight, so the scale reading is no greater than its weight under the stated condition.
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Вопрос
What is the SI unit of pressure?
Ответ
The pascal, Pa. One pascal equals 1 N/m².
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Вопрос
How do pressures compare at the same horizontal level in one connected static fluid?
Ответ
They are equal. Container shape does not change pressure at a fixed elevation.
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Вопрос
What does specific gravity compare?
Ответ
A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.
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Вопрос
How could collecting outflow test a volume flow rate predicted from area and average normal speed?
Ответ
Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.
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Вопрос
How does the particle model distinguish a fluid from a rigid solid?
Ответ
Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.
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Вопрос
At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?
Ответ
The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.
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Вопрос
A fully submerged object displaces 0.020 m³ of static water. Using ρ = 1000 kg/m³ and g = 10 m/s², what is F_B?
Ответ
200 N. F_B = ρgV = 1000×10×0.020.
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Вопрос
Why can a steel ship float even though steel is denser than water?
Ответ
Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.
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Вопрос
How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?
Ответ
Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.
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Вопрос
For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?
Ответ
Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.
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Вопрос
What does incompressible mean in the introductory ideal-fluid model?
Ответ
A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.
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Вопрос
At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?
Ответ
Pressure is lower at the higher point. P + ρgy remains constant.
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Вопрос
How can water displacement measure an irregular solid's volume?
Ответ
Submerge it fully and measure the increase in displaced-water volume. The volume change equals the submerged solid's volume if no water enters it.
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Вопрос
Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?
Ответ
The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.
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Вопрос
How can scale readings in air and water determine buoyant force?
Ответ
Subtract the immersed scale reading from the air reading. When the object is at rest and air buoyancy is negligible, the decrease equals the liquid's buoyant force.
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Вопрос
Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?
Ответ
30,000 Pa. P_gauge = ρgh = 1000×10×3.
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Вопрос
During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?
Ответ
The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.
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Вопрос
For a chosen fluid element in a horizontal region, what can a pressure difference do?
Ответ
It creates a net pressure force from higher pressure toward lower pressure and can accelerate the element by Newton's second law. Other forces must also be included when they matter.
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Вопрос
How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?
Ответ
Measure buoyant force while the object is fully submerged, then use V = F_B/(ρ_fluid g). The fluid density must be uniform over the displaced volume.
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Вопрос
A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?
Ответ
5,000 Pa. P = F/A = 200/0.040.
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Вопрос
Why doesn't a hydraulic lift multiply energy?
Ответ
The large-force piston moves a shorter distance. Ideally, input work equals output work.
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Вопрос
A large open tank has steady, incompressible, nonviscous efflux with negligible losses. Using g = 10 m/s², what speed leaves an opening 5 m below the surface when upper-surface speed is negligible?
Ответ
10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.
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Вопрос
An object floats first in water and then in a denser liquid. How does its submerged fraction change?
Ответ
It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

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