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

Cards in this deck

1. Card 1

   Question

   What separates a vector quantity from a scalar quantity?

   Answer

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

2. Card 2

   Question

   When is the point-object model useful in kinematics?

   Answer

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

3. Card 3

   Question

   When may the constant-acceleration kinematic equations be used?

   Answer

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

4. Card 4

   Question

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

   Answer

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

5. Card 5

   Question

   Why can horizontal and vertical projectile motion be analyzed separately?

   Answer

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

6. Card 6

   Question

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

   Answer

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

7. Card 7

   Question

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

   Answer

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

8. Card 8

   Question

   What makes a reference frame convenient for a motion problem?

   Answer

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

9. Card 9

   Question

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

   Answer

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

10. Card 10

    Question

    What does average velocity measure?

    Answer

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

11. Card 11

    Question

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

    Answer

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

12. Card 12

    Question

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

    Answer

    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.

13. Card 13

    Question

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

    Answer

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

14. Card 14

    Question

    What does average acceleration measure?

    Answer

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

15. Card 15

    Question

    What does a negative one-dimensional vector component mean?

    Answer

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

16. Card 16

    Question

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

    Answer

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

17. Card 17

    Question

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

    Answer

    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.

18. Card 18

    Question

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

    Answer

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

19. Card 19

    Question

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

    Answer

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

20. Card 20

    Question

    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?

    Answer

    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.

21. Card 21

    Question

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

    Answer

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

22. Card 22

    Question

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

    Answer

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

23. Card 23

    Question

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

    Answer

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

24. Card 24

    Question

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

    Answer

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

25. Card 25

    Question

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

    Answer

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

26. Card 26

    Question

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

    Answer

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

27. Card 27

    Question

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

    Answer

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

28. Card 28

    Question

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

    Answer

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

29. Card 29

    Question

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

    Answer

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

30. Card 30

    Question

    Can an object have nonzero velocity and zero acceleration?

    Answer

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

31. Card 31

    Question

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

    Answer

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

32. Card 32

    Question

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

    Answer

    Displacement. Area below the time axis contributes negative displacement.

33. Card 33

    Question

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

    Answer

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

34. Card 34

    Question

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

    Answer

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

35. Card 35

    Question

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

    Answer

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

36. Card 36

    Question

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

    Answer

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

37. Card 37

    Question

    How could video data test the independence of projectile components?

    Answer

    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.

38. Card 38

    Question

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

    Answer

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

39. Card 39

    Question

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

    Answer

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

40. Card 40

    Question

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

    Answer

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

41. Card 41

    Question

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

    Answer

    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.

42. Card 42

    Question

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

    Answer

    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.

43. Card 43

    Question

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

    Answer

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

44. Card 44

    Question

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

    Answer

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

45. Card 45

    Question

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

    Answer

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

46. Card 46

    Question

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

    Answer

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

47. Card 47

    Question

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

    Answer

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

48. Card 48

    Question

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

    Answer

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

49. Card 49

    Question

    What does translational equilibrium require?

    Answer

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

50. Card 50

    Question

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

    Answer

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

51. Card 51

    Question

    How do mass and weight differ?

    Answer

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

52. Card 52

    Question

    How does static friction choose its magnitude before slipping begins?

    Answer

    It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.

53. Card 53

    Question

    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?

    Answer

    F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.

54. Card 54

    Question

    What direction does centripetal acceleration point in circular motion?

    Answer

    Toward the circle's center. It changes the velocity's direction even when speed is constant.

55. Card 55

    Question

    What is the gravitational force magnitude between two point masses?

    Answer

    F_g = Gm₁m₂/r². Here r is the center-to-center separation.

56. Card 56

    Question

    Why isn't the normal force always equal to an object's weight?

    Answer

    It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.

57. Card 57

    Question

    What determines a friction coefficient in the simple model?

    Answer

    The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.

58. Card 58

    Question

    What is the centripetal-acceleration magnitude for speed v and radius r?

    Answer

    a_c = v²/r. It is a kinematic requirement, not a separate force.

59. Card 59

    Question

    An elevator accelerates upward. How does the scale reading compare with a rider's weight?

    Answer

    It is greater than the weight. Upward net force requires N - mg > 0.

60. Card 60

    Question

    What does a spring constant k measure, and what is its SI unit?

    Answer

    It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.

61. Card 61

    Question

    Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?

    Answer

    At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.

62. Card 62

    Question

    What provides centripetal force?

    Answer

    The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.

63. Card 63

    Question

    How is near-surface gravitational field strength related to weight?

    Answer

    F_g = mg. The local field strength g has units N/kg, equivalent to m/s².

64. Card 64

    Question

    How is weight resolved on an incline of angle θ measured from horizontal?

    Answer

    mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.

65. Card 65

    Question

    What does Newton's third law say about an interaction between objects A and B?

    Answer

    The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.

66. Card 66

    Question

    What does signed tangential acceleration describe during circular motion?

    Answer

    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.

67. Card 67

    Question

    What happens to gravitational force if the separation between two point masses doubles?

    Answer

    It becomes one-fourth as large. The force follows an inverse-square dependence on distance.

68. Card 68

    Question

    How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?

    Answer

    Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.

69. Card 69

    Question

    In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?

    Answer

    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.

70. Card 70

    Question

    Which tension components act for a conical pendulum?

    Answer

    The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.

71. Card 71

    Question

    What does apparent weight measure for an object supported by one surface?

    Answer

    The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.

72. Card 72

    Question

    How are several forces combined to find net force?

    Answer

    Add them as vectors, component by component. Opposing components subtract according to the chosen signs.

73. Card 73

    Question

    Why is tension uniform along one continuous ideal string?

    Answer

    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.

74. Card 74

    Question

    A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?

    Answer

    4 N. F_in = mv²/r = 0.5 × 16 / 2.

75. Card 75

    Question

    What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?

    Answer

    A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.

76. Card 76

    Question

    For the same net force, what happens to acceleration if mass doubles?

    Answer

    Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.

77. Card 77

    Question

    How do static and kinetic friction coefficients usually compare for the same pair of surfaces?

    Answer

    Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.

78. Card 78

    Question

    How are radial and tangential acceleration combined when circular speed changes?

    Answer

    Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).

79. Card 79

    Question

    A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?

    Answer

    It is twice as large. Surface field strength follows g = GM/R².

80. Card 80

    Question

    Does a force have to point in the direction of motion?

    Answer

    No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.

81. Card 81

    Question

    Where is the center of mass of a uniform object with a symmetric mass distribution?

    Answer

    At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.

82. Card 82

    Question

    How are speed, period, and frequency related in uniform circular motion?

    Answer

    v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.

83. Card 83

    Question

    Why is an object apparently weightless in free fall?

    Answer

    Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.

84. Card 84

    Question

    Can forces balance along one axis while an object accelerates along another?

    Answer

    Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.

85. Card 85

    Question

    Why don't Newton's third-law forces cancel on one object's free-body diagram?

    Answer

    Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.

86. Card 86

    Question

    On a frictionless banked curve, which force components create vertical balance and inward acceleration?

    Answer

    The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.

87. Card 87

    Question

    What motion results when the net force on an object is zero in an inertial frame?

    Answer

    Constant velocity. Rest is the special case with constant velocity equal to zero.

88. Card 88

    Question

    A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?

    Answer

    4 m/s². Use a = ΣF/m = 12/3.

89. Card 89

    Question

    What does the observed equivalence of inertial and gravitational mass imply for free fall?

    Answer

    Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.

90. Card 90

    Question

    Does friction in the simple dry-friction model depend on apparent contact area?

    Answer

    No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.

91. Card 91

    Question

    When should Hooke's-law predictions be treated cautiously?

    Answer

    When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.

92. Card 92

    Question

    What bank angle θ supports speed v on an ideal frictionless curve of radius r?

    Answer

    tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.

93. Card 93

    Question

    Why do internal forces cancel when finding the net force on a complete system?

    Answer

    They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.

94. Card 94

    Question

    An elevator moves downward at constant speed. How does the scale reading compare with weight?

    Answer

    It equals the weight. Constant velocity means zero acceleration and N - mg = 0.

95. Card 95

    Question

    What assumptions let an ideal pulley redirect a string without changing its tension magnitude?

    Answer

    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.

96. Card 96

    Question

    What does inertia describe?

    Answer

    An object's resistance to changes in velocity. Mass measures translational inertia.

97. Card 97

    Question

    For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?

    Answer

    Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.

98. Card 98

    Question

    Does zero net force mean no forces act?

    Answer

    No. Several forces can act and cancel vectorially.

99. Card 99

    Question

    What is the common model for kinetic-friction magnitude?

    Answer

    f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.

100. Card 100

     Question

     How could hanging masses measure the spring constant of one ideal spring?

     Answer

     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.

101. Card 101

     Question

     For the same object at the same circular radius, how does required inward net force change if speed doubles?

     Answer

     It becomes four times as large. F_in = mv²/r depends on speed squared.

102. Card 102

     Question

     Where is the center of mass of two point masses on an x-axis?

     Answer

     At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.

103. Card 103

     Question

     Why must net force, rather than one selected force, be used in ΣF = ma?

     Answer

     All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.

104. Card 104

     Question

     Why can tension vary along a hanging chain with nonnegligible mass?

     Answer

     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.

105. Card 105

     Question

     What makes a reference frame inertial?

     Answer

     An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.

106. Card 106

     Question

     How could carts test the proportionality between acceleration and net force?

     Answer

     Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.

107. Card 107

     Question

     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?

     Answer

     T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.

108. Card 108

     Question

     Which direction does kinetic friction act?

     Answer

     Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.

109. Card 109

     Question

     What does the slope of a spring-force-versus-displacement graph give?

     Answer

     -k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.

110. Card 110

     Question

     What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?

     Answer

     v_min = √(gr). At the threshold, the support force or tension is zero.

111. Card 111

     Question

     What is translational kinetic energy?

     Answer

     Energy associated with an object's translational motion. For a point-like object, K = ½mv².

112. Card 112

     Question

     How is work by a constant force calculated when its point of application undergoes a straight displacement?

     Answer

     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.

113. Card 113

     Question

     What does power measure?

     Answer

     The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.

114. Card 114

     Question

     What does conservation of energy say for an isolated system?

     Answer

     The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.

115. Card 115

     Question

     Can translational kinetic energy be negative?

     Answer

     No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.

116. Card 116

     Question

     What does negative work by a force mean?

     Answer

     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.

117. Card 117

     Question

     What is the near-surface change in gravitational potential energy?

     Answer

     ΔU_g = mgΔy. It applies when g can be treated as constant.

118. Card 118

     Question

     When is a chosen system's mechanical energy K + U conserved?

     Answer

     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.

119. Card 119

     Question

     What is the SI unit of power?

     Answer

     The watt, W. One watt equals one joule per second.

120. Card 120

     Question

     For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?

     Answer

     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.

121. Card 121

     Question

     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?

     Answer

     v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².

122. Card 122

     Question

     Does choosing a different zero level for potential energy change physical predictions?

     Answer

     No. Only potential-energy differences enter measurable energy changes.

123. Card 123

     Question

     Can an engine do the same work with different average power?

     Answer

     Yes. Doing the same work in less time requires greater average power.

124. Card 124

     Question

     When does a constant nonzero force do zero work over an interval?

     Answer

     When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.

125. Card 125

     Question

     A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?

     Answer

     No. With only gravity doing work, the potential-energy change depends on height, not path.

126. Card 126

     Question

     How does translational kinetic energy change if speed doubles at constant mass?

     Answer

     It becomes four times as large. Kinetic energy depends on v².

127. Card 127

     Question

     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?

     Answer

     U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.

128. Card 128

     Question

     What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?

     Answer

     Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.

129. Card 129

     Question

     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?

     Answer

     14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.

130. Card 130

     Question

     What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?

     Answer

     The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.

131. Card 131

     Question

     A machine transfers 600 J in 3 s. What is its average power?

     Answer

     200 W. Divide energy transferred by elapsed time.

132. Card 132

     Question

     Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?

     Answer

     The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.

133. Card 133

     Question

     A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?

     Answer

     At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.

134. Card 134

     Question

     Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?

     Answer

     They are equal. Kinetic energy uses speed and has no direction.

135. Card 135

     Question

     What makes work by a conservative force path independent?

     Answer

     It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.

136. Card 136

     Question

     A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?

     Answer

     30 J. Here θ = 0, so W = Fd = 10×3.

137. Card 137

     Question

     How is total potential energy built for a system with several interacting pairs?

     Answer

     Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.

138. Card 138

     Question

     How should external work appear in an energy equation?

     Answer

     As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.

139. Card 139

     Question

     How does a spring launch problem combine energy forms?

     Answer

     Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.

140. Card 140

     Question

     For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?

     Answer

     P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.

141. Card 141

     Question

     How does translational kinetic energy change if mass triples at constant speed?

     Answer

     It triples. Kinetic energy is directly proportional to mass.

142. Card 142

     Question

     How much net work does a conservative force do around a path that returns to the initial configuration?

     Answer

     Zero. The initial and final potential energies are the same.

143. Card 143

     Question

     Where is stable equilibrium on a potential-energy-versus-position graph?

     Answer

     At a local minimum. Small displacements produce forces that point back toward the minimum.

144. Card 144

     Question

     Which displacement belongs in the work done by a force on a rigid object?

     Answer

     The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.

145. Card 145

     Question

     What happens to mechanical energy when kinetic friction acts inside the chosen system?

     Answer

     Some mechanical energy becomes thermal energy. The broader system's total energy still balances.

146. Card 146

     Question

     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?

     Answer

     Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.

147. Card 147

     Question

     If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?

     Answer

     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.

148. Card 148

     Question

     How can force-sensor data measure work when force changes as its point of application moves?

     Answer

     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.

149. Card 149

     Question

     Why is potential energy assigned to a system rather than one isolated object?

     Answer

     It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.

150. Card 150

     Question

     How can work by a nonconservative force depend on path?

     Answer

     Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.

151. Card 151

     Question

     A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?

     Answer

     9 J. K = ½(2)(3²) = 9 J.

152. Card 152

     Question

     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?

     Answer

     W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.

153. Card 153

     Question

     A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?

     Answer

     +100 J. ΔU_g = mgΔy = 2 × 10 × 5.

154. Card 154

     Question

     Why are energy bar charts useful?

     Answer

     They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.

155. Card 155

     Question

     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?

     Answer

     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.

156. Card 156

     Question

     A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?

     Answer

     6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².

157. Card 157

     Question

     Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?

     Answer

     Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.

158. Card 158

     Question

     What does a steep potential-energy graph imply about force magnitude in one dimension?

     Answer

     A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).

159. Card 159

     Question

     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?

     Answer

     10 J. U_s = ½(80)(0.50²).

160. Card 160

     Question

     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?

     Answer

     200 W. P = Fv_point = 50 × 4.

161. Card 161

     Question

     If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?

     Answer

     They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.

162. Card 162

     Question

     Does an object's translational kinetic energy depend on the reference frame?

     Answer

     Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.

163. Card 163

     Question

     Why can work depend on the system boundary?

     Answer

     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.

164. Card 164

     Question

     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?

     Answer

     12 J. The signed area is ½×4×6.

165. Card 165

     Question

     A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?

     Answer

     +38 J. Add the signed transfers across the boundary: 50 J - 12 J.

166. Card 166

     Question

     What is the clearest first step in an energy-conservation problem?

     Answer

     Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.

167. Card 167

     Question

     Why can energy methods solve some problems without finding time?

     Answer

     Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.

168. Card 168

     Question

     Why can a force's instantaneous mechanical power be zero while the force is nonzero?

     Answer

     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.

169. Card 169

     Question

     What is the SI unit of kinetic energy?

     Answer

     The joule, J. One joule equals 1 kg·m²/s².

170. Card 170

     Question

     How is work by a conservative force related to potential-energy change?

     Answer

     W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.

171. Card 171

     Question

     Where is unstable equilibrium on a potential-energy-versus-position graph?

     Answer

     At a local maximum. A small displacement produces a force that pushes the system farther away.

172. Card 172

     Question

     For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?

     Answer

     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.

173. Card 173

     Question

     Why should thermal energy not be written as a force?

     Answer

     Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.

174. Card 174

     Question

     How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?

     Answer

     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.

175. Card 175

     Question

     According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?

     Answer

     Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.

176. Card 176

     Question

     What is linear momentum?

     Answer

     p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.

177. Card 177

     Question

     How is a multi-object system's total momentum found?

     Answer

     Add every object's momentum as a vector. In one dimension, add signed values.

178. Card 178

     Question

     For a chosen object or system, what is external impulse?

     Answer

     The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.

179. Card 179

     Question

     What experimental uncertainty matters strongly when comparing collision kinetic energies?

     Answer

     Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.

180. Card 180

     Question

     Why can two objects bounce apart yet still collide inelastically?

     Answer

     Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.

181. Card 181

     Question

     A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?

     Answer

     +12 kg·m/s. p = mv = 3 × 4.

182. Card 182

     Question

     Why can momentum be negative while kinetic energy cannot?

     Answer

     Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.

183. Card 183

     Question

     When is a system's total linear momentum conserved?

     Answer

     When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.

184. Card 184

     Question

     Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?

     Answer

     They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.

185. Card 185

     Question

     Can total kinetic energy increase in an explosion?

     Answer

     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.

186. Card 186

     Question

     How is total momentum related to center-of-mass velocity?

     Answer

     p_total = Mv_cm. M is the system's total mass.

187. Card 187

     Question

     How does a nonzero external impulse affect system momentum?

     Answer

     It changes total momentum by that impulse. J_external = Δp_system.

188. Card 188

     Question

     Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?

     Answer

     They are equal in magnitude and opposite in direction. The system began with zero total momentum.

189. Card 189

     Question

     What are equivalent SI units for impulse?

     Answer

     N·s and kg·m/s. Both represent a change in momentum.

190. Card 190

     Question

     What defines an elastic collision?

     Answer

     Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.

191. Card 191

     Question

     How can a force sensor and motion detector test the impulse–momentum theorem for one cart?

     Answer

     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.

192. Card 192

     Question

     A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?

     Answer

     Left. The person and boat acquire opposite momenta so total momentum remains zero.

193. Card 193

     Question

     Why must momentum signs be kept through an impulse calculation?

     Answer

     Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.

194. Card 194

     Question

     What defines a perfectly inelastic collision?

     Answer

     The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.

195. Card 195

     Question

     Why can momentum be conserved during a collision even when large forces act?

     Answer

     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.

196. Card 196

     Question

     Two objects have equal speed. Which has the larger momentum magnitude?

     Answer

     The object with larger mass. At equal speed, momentum is proportional to mass.

197. Card 197

     Question

     How is momentum conservation written for a two-dimensional isolated interaction?

     Answer

     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.

198. Card 198

     Question

     For a chosen object or system, how is average net external force related to impulse?

     Answer

     F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.

199. Card 199

     Question

     Which conservation law alone can determine the shared final velocity of a sticking collision?

     Answer

     Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.

200. Card 200

     Question

     Two equal momentum vectors point along +x and +y. What direction does their total momentum point?

     Answer

     At 45° between the positive axes. Equal perpendicular components produce that resultant direction.

     

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201. Card 201

     Question

     If external impulse during a collision is small but not zero, what should experimental data show?

     Answer

     Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.

202. Card 202

     Question

     A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?

     Answer

     It does not change. Impulse depends on total signed area, not peak force alone.

203. Card 203

     Question

     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?

     Answer

     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.

204. Card 204

     Question

     How can a nearly frictionless cart track improve a momentum-conservation test?

     Answer

     It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.

205. Card 205

     Question

     How does an object's momentum change if its speed doubles at constant mass?

     Answer

     Its momentum magnitude doubles. Momentum depends linearly on speed.

206. Card 206

     Question

     For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?

     Answer

     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.

207. Card 207

     Question

     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?

     Answer

     The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.

208. Card 208

     Question

     Why is sticking evidence of an inelastic collision?

     Answer

     The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.

209. Card 209

     Question

     Can a moving two-object system have zero total momentum?

     Answer

     Yes. Equal and opposite momenta cancel even though each object is moving.

210. Card 210

     Question

     A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?

     Answer

     3 N·s in the force direction. Multiply the net external force by the interaction time.

211. Card 211

     Question

     What does a momentum-versus-velocity graph's slope represent for one object?

     Answer

     Its mass. The relationship p = mv is linear through the origin.

212. Card 212

     Question

     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?

     Answer

     +2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).

213. Card 213

     Question

     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?

     Answer

     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.

214. Card 214

     Question

     A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?

     Answer

     -8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).

215. Card 215

     Question

     What remains conserved in an isolated inelastic collision?

     Answer

     Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.

216. Card 216

     Question

     Why does choosing both colliding objects as the system simplify momentum analysis?

     Answer

     Their contact forces become internal. Only external impulse can change the system total.

217. Card 217

     Question

     For a chosen object or system, what does the slope of its momentum-versus-time graph represent?

     Answer

     Net external force. A steeper slope means a larger force in the slope's signed direction.

218. Card 218

     Question

     Why do airbags reduce injury force during a stop?

     Answer

     They increase the stopping time for roughly the same momentum change. That lowers the average force.

219. Card 219

     Question

     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?

     Answer

     2 m/s. Momentum 4 kg·m/s is shared by 2 kg.

220. Card 220

     Question

     For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?

     Answer

     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.

221. Card 221

     Question

     What is angular displacement?

     Answer

     The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.

222. Card 222

     Question

     For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?

     Answer

     Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.

223. Card 223

     Question

     For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?

     Answer

     Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.

224. Card 224

     Question

     What does rotational inertia measure?

     Answer

     Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.

225. Card 225

     Question

     What is the lever arm in a torque calculation?

     Answer

     The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.

226. Card 226

     Question

     For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?

     Answer

     ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.

227. Card 227

     Question

     Two points lie on the same rotating rigid disk. Which rotational quantities are the same?

     Answer

     They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.

228. Card 228

     Question

     How is rotational inertia found for a collection of point masses?

     Answer

     I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.

229. Card 229

     Question

     What determines the magnitude of torque from one force about a chosen axis?

     Answer

     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.

230. Card 230

     Question

     What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?

     Answer

     Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.

231. Card 231

     Question

     For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?

     Answer

     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.

232. Card 232

     Question

     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?

     Answer

     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.

233. Card 233

     Question

     At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?

     Answer

     Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.

234. Card 234

     Question

     How are clockwise and counterclockwise torques combined?

     Answer

     Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.

235. Card 235

     Question

     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?

     Answer

     Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.

236. Card 236

     Question

     Why must an axis be named when stating rotational inertia?

     Answer

     The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.

237. Card 237

     Question

     For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?

     Answer

     Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.

238. Card 238

     Question

     Why is torque's unit N·m not called a joule?

     Answer

     Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.

239. Card 239

     Question

     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?

     Answer

     4 rad/s². |α| = |Στ_external|/I = 8/2.

240. Card 240

     Question

     Where can the weight of a rigid object be treated as acting in a uniform gravitational field?

     Answer

     At the object's center of mass. That single force gives the same net gravitational force and torque.

241. Card 241

     Question

     For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?

     Answer

     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.

242. Card 242

     Question

     For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?

     Answer

     Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.

243. Card 243

     Question

     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?

     Answer

     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.

244. Card 244

     Question

     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?

     Answer

     Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.

245. Card 245

     Question

     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?

     Answer

     The hoop. More of its mass lies far from the axis.

246. Card 246

     Question

     Why can a rigid object have zero net external force but nonzero net external torque?

     Answer

     External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.

247. Card 247

     Question

     Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?

     Answer

     ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.

248. Card 248

     Question

     A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?

     Answer

     4 N·m. τ = rF for a perpendicular force.

249. Card 249

     Question

     For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?

     Answer

     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.

250. Card 250

     Question

     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?

     Answer

     Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.

251. Card 251

     Question

     For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?

     Answer

     Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.

252. Card 252

     Question

     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?

     Answer

     The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.

253. Card 253

     Question

     A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?

     Answer

     The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.

254. Card 254

     Question

     Does moving the chosen pivot change an individual force's torque?

     Answer

     Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.

255. Card 255

     Question

     How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?

     Answer

     I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.

256. Card 256

     Question

     How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?

     Answer

     Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.

257. Card 257

     Question

     For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?

     Answer

     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.

258. Card 258

     Question

     How could a meterstick experiment test torque balance?

     Answer

     Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.

259. Card 259

     Question

     For uniform rotation at frequency f, what is the angular-speed magnitude?

     Answer

     |ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.

260. Card 260

     Question

     Why is choosing the pivot at an unknown support force often useful?

     Answer

     That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.

261. Card 261

     Question

     Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?

     Answer

     The parallel axis through the center of mass. Any offset adds the positive term Md².

262. Card 262

     Question

     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?

     Answer

     It becomes one-third as large. For each stated system, α = Στ_external/I.

263. Card 263

     Question

     A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?

     Answer

     3 m/s. v_t = r|ω| = 0.50 × 6.

264. Card 264

     Question

     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?

     Answer

     3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.

265. Card 265

     Question

     For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?

     Answer

     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.

266. Card 266

     Question

     A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?

     Answer

     6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.

267. Card 267

     Question

     How does moving mass farther from a rotation axis affect rotational inertia?

     Answer

     It increases rotational inertia strongly. For a point mass, I = mr².

268. Card 268

     Question

     How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?

     Answer

     Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.

269. Card 269

     Question

     Why must angular displacement be in radians for Δs = rΔθ?

     Answer

     Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.

270. Card 270

     Question

     When does a nonzero force produce zero torque about an axis?

     Answer

     When its line of action passes through the axis. The lever arm is then zero.

271. Card 271

     Question

     What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?

     Answer

     L = Iω about that axis. Use one signed-axis convention consistently for L and ω.

272. Card 272

     Question

     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?

     Answer

     v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.

273. Card 273

     Question

     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?

     Answer

     W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.

274. Card 274

     Question

     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?

     Answer

     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.

275. Card 275

     Question

     When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?

     Answer

     When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.

276. Card 276

     Question

     What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?

     Answer

     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.

277. Card 277

     Question

     What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?

     Answer

     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.

278. Card 278

     Question

     For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?

     Answer

     Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.

279. Card 279

     Question

     What is a rigid body's rotational kinetic energy about a fixed axis?

     Answer

     K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.

280. Card 280

     Question

     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)?

     Answer

     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)).

281. Card 281

     Question

     How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?

     Answer

     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.

282. Card 282

     Question

     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?

     Answer

     K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).

283. Card 283

     Question

     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?

     Answer

     P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.

284. Card 284

     Question

     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?

     Answer

     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.

285. Card 285

     Question

     Does angular-momentum conservation require rotational kinetic-energy conservation?

     Answer

     No. Internal work can change rotational kinetic energy while angular momentum stays constant.

286. Card 286

     Question

     Why do astronauts feel weightless in orbit even though gravity acts on them?

     Answer

     They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.

287. Card 287

     Question

     Two wheels spin at the same angular speed. Which has more rotational kinetic energy?

     Answer

     The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.

288. Card 288

     Question

     For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?

     Answer

     Net external torque on the system about that axis. A constant slope means constant signed net external torque there.

289. Card 289

     Question

     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?

     Answer

     120 W. Using signed quantities about the shaft axis, P = τω = 12×10.

290. Card 290

     Question

     While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?

     Answer

     No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.

291. Card 291

     Question

     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?

     Answer

     v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.

292. Card 292

     Question

     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?

     Answer

     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.

293. Card 293

     Question

     For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?

     Answer

     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.

294. Card 294

     Question

     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?

     Answer

     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.

295. Card 295

     Question

     For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?

     Answer

     It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.

296. Card 296

     Question

     How does rotational kinetic energy change if angular speed doubles at fixed I?

     Answer

     It becomes four times as large. Rotational kinetic energy depends on ω².

297. Card 297

     Question

     Why should external torque be evaluated about the same axis used for angular momentum?

     Answer

     Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.

298. Card 298

     Question

     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?

     Answer

     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.

299. Card 299

     Question

     Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?

     Answer

     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.

300. Card 300

     Question

     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?

     Answer

     v = √(GM/r). Gravity supplies the inward net force.

301. Card 301

     Question

     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?

     Answer

     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.

302. Card 302

     Question

     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?

     Answer

     Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.

303. Card 303

     Question

     Why can't the rolling condition alone prove that friction points uphill or downhill?

     Answer

     Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.

304. Card 304

     Question

     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?

     Answer

     E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.

305. Card 305

     Question

     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?

     Answer

     Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.

306. Card 306

     Question

     What makes simple harmonic motion a special kind of periodic motion?

     Answer

     Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.

307. Card 307

     Question

     What does the amplitude of an SHM displacement graph represent?

     Answer

     The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.

308. Card 308

     Question

     How are period and frequency related?

     Answer

     T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.

309. Card 309

     Question

     What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?

     Answer

     T = 2π√(m/k). The motion must stay in the spring's linear SHM range.

310. Card 310

     Question

     For one-dimensional SHM, what is the equilibrium position?

     Answer

     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.

311. Card 311

     Question

     How far apart in phase are displacement and velocity in SHM?

     Answer

     One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.

312. Card 312

     Question

     When can a simple pendulum be modeled as SHM?

     Answer

     For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.

313. Card 313

     Question

     An oscillator completes 12 cycles in 6 s. What are its frequency and period?

     Answer

     f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.

314. Card 314

     Question

     For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?

     Answer

     U_s = ½kx². It has the same value at +x and -x.

315. Card 315

     Question

     At the equilibrium position of SHM, is the oscillator necessarily at rest?

     Answer

     No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.

316. Card 316

     Question

     How does a spring oscillator's period change if k becomes four times as large?

     Answer

     The period is halved. T is proportional to 1/√k.

317. Card 317

     Question

     How are acceleration and displacement related along the SHM coordinate?

     Answer

     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.

318. Card 318

     Question

     For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?

     Answer

     E = ½kA². It stays constant when dissipative effects are negligible.

319. Card 319

     Question

     In a small-angle pendulum, where are speed and gravitational potential energy greatest?

     Answer

     Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.

320. Card 320

     Question

     How can frequency be read from an oscillation-versus-time graph?

     Answer

     Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.

321. Card 321

     Question

     Why does an ideal mass–spring oscillator exhibit SHM?

     Answer

     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.

322. Card 322

     Question

     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?

     Answer

     1 J. E = ½(50)(0.20²).

323. Card 323

     Question

     At maximum positive displacement in SHM, what are velocity and acceleration?

     Answer

     Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.

324. Card 324

     Question

     How does a spring oscillator's period change if its mass becomes four times as large?

     Answer

     The period doubles. T is proportional to √m.

325. Card 325

     Question

     Why isn't uniform circular motion itself one-dimensional SHM?

     Answer

     The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.

326. Card 326

     Question

     For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?

     Answer

     It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².

327. Card 327

     Question

     In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?

     Answer

     Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.

328. Card 328

     Question

     Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?

     Answer

     No within the ideal SHM model. The period depends on system parameters, not amplitude.

329. Card 329

     Question

     How is maximum speed related to amplitude and angular frequency in SHM?

     Answer

     v_max = ωA. Maximum speed occurs at equilibrium.

330. Card 330

     Question

     For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?

     Answer

     K = ½k(A² - x²). Subtract spring potential energy from the constant total.

331. Card 331

     Question

     How far apart in phase are displacement and acceleration in SHM?

     Answer

     Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.

332. Card 332

     Question

     What is the period of a small-angle simple pendulum of length L when damping is negligible?

     Answer

     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.

333. Card 333

     Question

     If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?

     Answer

     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.

334. Card 334

     Question

     At equilibrium, how are a horizontal ideal spring oscillator's energies divided?

     Answer

     Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.

335. Card 335

     Question

     An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?

     Answer

     Both are positive. Motion and restoring acceleration point right toward equilibrium.

336. Card 336

     Question

     How does a pendulum's period change if its length becomes nine times as large?

     Answer

     The period triples. T is proportional to √L.

337. Card 337

     Question

     If SHM starts at maximum positive displacement, what equation gives its position?

     Answer

     x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.

338. Card 338

     Question

     What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?

     Answer

     A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.

339. Card 339

     Question

     At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?

     Answer

     Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.

340. Card 340

     Question

     For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?

     Answer

     Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.

341. Card 341

     Question

     What makes a substance a fluid?

     Answer

     It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.

342. Card 342

     Question

     What is mass density?

     Answer

     Mass per volume: ρ = m/V. Its SI unit is kg/m³.

343. Card 343

     Question

     For pressure that is uniform over a surface patch, how is it related to normal force and area?

     Answer

     P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.

344. Card 344

     Question

     What is volume flow rate?

     Answer

     Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.

345. Card 345

     Question

     What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?

     Answer

     The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.

346. Card 346

     Question

     What conditions support the basic Bernoulli model used here?

     Answer

     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.

347. Card 347

     Question

     Under the ideal model, how does average density predict whether a free object floats or sinks?

     Answer

     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.

348. Card 348

     Question

     How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?

     Answer

     Q = Av. This gives the volume crossing a completely filled pipe section per time.

349. Card 349

     Question

     How does a static fluid exert force on a surface?

     Answer

     Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.

350. Card 350

     Question

     How does pressure change with depth in a static uniform fluid?

     Answer

     It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.

351. Card 351

     Question

     What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?

     Answer

     F_B = mg. The object's weight equals the weight of the fluid it displaces.

352. Card 352

     Question

     What is the continuity equation for steady incompressible flow in one filled pipe?

     Answer

     A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.

353. Card 353

     Question

     Why does a static fluid produce an upward buoyant force?

     Answer

     Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.

354. Card 354

     Question

     What is the absolute pressure at depth h below the open surface of a static, uniform liquid?

     Answer

     P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.

355. Card 355

     Question

     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?

     Answer

     Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.

356. Card 356

     Question

     Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?

     Answer

     0.060 m³/s. Q = Av = 0.020×3.

357. Card 357

     Question

     What does the slope of a mass-versus-volume graph represent for one uniform material?

     Answer

     Density. Since m = ρV, the line's slope is ρ.

358. Card 358

     Question

     How do gauge pressure and absolute pressure differ?

     Answer

     Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.

359. Card 359

     Question

     For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?

     Answer

     No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.

360. Card 360

     Question

     For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?

     Answer

     It doubles. Continuity keeps Av constant.

361. Card 361

     Question

     When does a fluid element's velocity change?

     Answer

     Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.

362. Card 362

     Question

     For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?

     Answer

     Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.

363. Card 363

     Question

     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?

     Answer

     V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.

364. Card 364

     Question

     For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?

     Answer

     It becomes four times as large. Area is proportional to radius squared.

365. Card 365

     Question

     What does Pascal's principle say for a confined incompressible fluid at rest?

     Answer

     An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.

366. Card 366

     Question

     In a uniform static fluid, what does the slope of gauge pressure versus depth represent?

     Answer

     ρg. For known g, the slope can determine fluid density.

367. Card 367

     Question

     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?

     Answer

     Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.

368. Card 368

     Question

     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?

     Answer

     8 m/s. Continuity gives v₂ = A₁v₁/A₂.

369. Card 369

     Question

     What physical quantity does each term in P + ½ρv² + ρgy share?

     Answer

     Energy per unit volume, equivalent to pressure. Every term uses units of pascals.

370. Card 370

     Question

     In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?

     Answer

     Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.

371. Card 371

     Question

     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?

     Answer

     0.75, or 75%. Use the density ratio for floating equilibrium.

372. Card 372

     Question

     A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?

     Answer

     Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.

373. Card 373

     Question

     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?

     Answer

     v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.

374. Card 374

     Question

     Why does the same force create more pressure on a smaller area?

     Answer

     Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.

375. Card 375

     Question

     A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?

     Answer

     3.0×10³ kg/m³. Divide mass by volume.

376. Card 376

     Question

     What conservation law underlies the continuity equation for incompressible flow?

     Answer

     Conservation of mass. Constant density turns equal mass flow into equal volume flow.

377. Card 377

     Question

     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?

     Answer

     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.

378. Card 378

     Question

     What is the SI unit of pressure?

     Answer

     The pascal, Pa. One pascal equals 1 N/m².

379. Card 379

     Question

     How do pressures compare at the same horizontal level in one connected static fluid?

     Answer

     They are equal. Container shape does not change pressure at a fixed elevation.

380. Card 380

     Question

     What does specific gravity compare?

     Answer

     A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.

381. Card 381

     Question

     How could collecting outflow test a volume flow rate predicted from area and average normal speed?

     Answer

     Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.

382. Card 382

     Question

     How does the particle model distinguish a fluid from a rigid solid?

     Answer

     Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.

383. Card 383

     Question

     At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?

     Answer

     The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.

384. Card 384

     Question

     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?

     Answer

     200 N. F_B = ρgV = 1000×10×0.020.

385. Card 385

     Question

     Why can a steel ship float even though steel is denser than water?

     Answer

     Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.

386. Card 386

     Question

     How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?

     Answer

     Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.

387. Card 387

     Question

     For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?

     Answer

     Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.

388. Card 388

     Question

     What does incompressible mean in the introductory ideal-fluid model?

     Answer

     A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.

389. Card 389

     Question

     At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?

     Answer

     Pressure is lower at the higher point. P + ρgy remains constant.

390. Card 390

     Question

     How can water displacement measure an irregular solid's volume?

     Answer

     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.

391. Card 391

     Question

     Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?

     Answer

     The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.

392. Card 392

     Question

     How can scale readings in air and water determine buoyant force?

     Answer

     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.

393. Card 393

     Question

     Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?

     Answer

     30,000 Pa. P_gauge = ρgh = 1000×10×3.

394. Card 394

     Question

     During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?

     Answer

     The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.

395. Card 395

     Question

     For a chosen fluid element in a horizontal region, what can a pressure difference do?

     Answer

     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.

396. Card 396

     Question

     How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?

     Answer

     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.

397. Card 397

     Question

     A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?

     Answer

     5,000 Pa. P = F/A = 200/0.040.

398. Card 398

     Question

     Why doesn't a hydraulic lift multiply energy?

     Answer

     The large-force piston moves a shorter distance. Ideally, input work equals output work.

399. Card 399

     Question

     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?

     Answer

     10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.

400. Card 400

     Question

     An object floats first in water and then in a denser liquid. How does its submerged fraction change?

     Answer

     It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

400 cards

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

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