AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 6: Energy & Momentum of Rotating SystemsExamples of Rotational Systems

Examples of Rotational Systems (College Board AP® Physics 1: Algebra-Based): Exam Questions

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Examples of Rotational Systems

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11 mark

A comet moves in a highly elliptical orbit around the Sun.

Which of the following quantities are conserved for the comet in its orbit?

  • Linear momentum

  • Angular momentum

  • Gravitational potential energy

  • Rotational kinetic energy

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2
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A wheel of mass M, radius R, and rotational inertia I rolls across the ground without slipping with translational kinetic energy K.

Which of the following expressions represents the rotational kinetic energy of the wheel?

  • K

  • K over 2

  • K open parentheses fraction numerator I over denominator M R squared end fraction close parentheses

  • K open parentheses fraction numerator M R squared over denominator I end fraction close parentheses

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3
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Diagram showing an elliptical orbit around a central grey circle. Points A, B, C, and D are marked on the orbit, denoting different positions.

A planet orbits a star in an elliptical orbit, as shown in the figure.

At which of the positions on the figure does the planet have the greatest speed?

    Choose your answer

    4
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    A spaceship is launched from the surface of the Earth.

    Which of the following does not affect the escape velocity of the spaceship at the Earth's surface?

    • The mass of the Earth.

    • The radius of the Earth.

    • The mass of the spaceship.

    • The gravitational field strength at the Earth's surface.

    Choose your answer

    5
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    Graph with three energy curves labeled 1, 2, and 3 versus distance r. Curve 1 is positive, while 2 and 3 are negative.

    The graph shows the energy of a satellite in a circular orbit as a function of distance r from the center of the Earth.

    Which of the curves labeled 1, 2, and 3 represent the kinetic energy K, potential energy U, and total energy E of the satellite?

    Curve 1

    Curve 2

    Curve 3

    A

    U

    K

    E

    B

    K

    E

    U

    C

    E

    K

    U

    D

    K

    U

    E

      Choose your answer

      1
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      Two planets, X and Y, have the same mass. Planet X has a greater surface gravity than Planet Y.

      Which planet has a greater escape velocity?

      • Planet X has a greater escape velocity.

      • Planet Y has a greater escape velocity.

      • Both planets have the same escape velocity.

      • There is not enough information to determine which planet has a greater escape velocity.

      Choose your answer

      2
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      A bowling ball of mass 5.0 space kg and radius 12.0 space cm rolls along a horizontal surface with a velocity of 8 space straight m divided by straight s. The ball is a solid sphere with a rotational inertia of I space equals space 2 over 5 m r squared.

      Which of the following is most nearly the total kinetic energy of the bowling ball?

      • 60 space straight J

      • 120 space straight J

      • 160 space straight J

      • 220 space straight J

      Choose your answer

      3
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      A hollow cylinder and a solid cylinder positioned at the top of an inclined plane, with labels pointing to each cylinder.

      A hollow cylinder and a solid cylinder of the same mass and radius are released from rest at the top of an inclined ramp. Both roll down the ramp without slipping.

      Which cylinder reaches the bottom of the ramp first, and why?

      • The hollow cylinder, because it gains less rotational kinetic energy than the solid cylinder

      • The hollow cylinder, because it loses less mechanical energy due to friction than the solid cylinder

      • The solid cylinder, because it gains less rotational kinetic energy than the hollow cylinder

      • The solid cylinder, because it loses less mechanical energy due to friction than the hollow cylinder

      Choose your answer

      4
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      Two satellites, X and Y, of equal mass, orbit a planet at radii R and 2 R respectively.

      Which one of the following statements is true about the kinetic and potential energies of the satellites?

      • Satellite X has more kinetic energy and more potential energy than satellite Y.

      • Satellite X has more kinetic energy and less potential energy than satellite Y.

      • Satellite X has less kinetic energy and more potential energy than satellite Y.

      • Satellite X has less kinetic energy and less potential energy than satellite Y.

      Choose your answer

      5
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      A soccer ball of mass m and radius r rolls along a horizontal surface without slipping. The soccer ball can be modeled as a hollow sphere of rotational inertia 2 over 3 m r squared.

      Which of the following is most nearly the proportion the rotational kinetic energy contributes to the total kinetic energy of the soccer ball?

      • 20 percent sign

      • 40 percent sign

      • 60 percent sign

      • 80 percent sign

      Choose your answer

      1
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      A solid ball of mass M and radius R has rotational inertia 2 over 5 M R squared about its center. It rolls without slipping along a level surface at speed v just before it begins rolling up an inclined plane.

      Which of the following expressions correctly represents the maximum vertical height the solid ball can ascend to when it rolls up the incline without slipping?

      • fraction numerator v squared over denominator 5 g end fraction

      • fraction numerator 2 v squared over denominator 5 g end fraction

      • fraction numerator v squared over denominator 2 g end fraction

      • fraction numerator 7 v squared over denominator 10 g end fraction

      Choose your answer

      2
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      A probe is launched vertically upwards from the Earth's surface with a velocity equal to half the required escape velocity from this point.

      If the radius of the Earth is R, which of the following expressions correctly describes the maximum height reached by the probe?

      • R over 3

      • R over 2

      • R

      • 2 R

      Choose your answer

      3
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      A satellite of mass m is initially in a circular orbit of radius r subscript 1 around the Earth, which has a radius of R and surface gravity g.

      Which of the following correctly describes the work done by gravity when a satellite is moved from its initial orbital radius r subscript 1 to a larger orbital radius r subscript 2?

      • The work done by gravity is positive and equal to fraction numerator m g r subscript 2 open parentheses r subscript 2 space minus space r subscript 1 close parentheses over denominator r subscript 1 end fraction

      • The work done by gravity is negative and equal to fraction numerator m g r subscript 2 open parentheses r subscript 2 space minus space r subscript 1 close parentheses over denominator r subscript 1 end fraction

      • The work done by gravity is positive and equal to fraction numerator m g R squared open parentheses r subscript 2 space minus space r subscript 1 close parentheses over denominator 2 r subscript 2 r subscript 1 end fraction

      • The work done by gravity is negative and equal to fraction numerator m g R squared open parentheses r subscript 2 space minus space r subscript 1 close parentheses over denominator 2 r subscript 2 r subscript 1 end fraction

      Choose your answer

      4
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      Energy bar chart with three labels Ug, Kt, and Kr. Ug bar has the maximum possible value (3 units), Kt and Kr are zero.

      In Experiment 1, a solid disk of rotational inertia 1 half m r squared is released from rest at the top of a ramp where the frictional force is such that the disk rolls without slipping. In Experiment 2, the same disk is released from rest at the top of an identically shaped ramp where the frictional force is such that the disk rolls and slips. The energy bar chart in the figure represents the gravitational potential energy U subscript g of the disk-Earth systems, and the translational kinetic energy K subscript t and rotational kinetic energy K subscript r of the disks just before their release.

      Which of the following graphs could represent the energy bar charts for the disks at the bottom of the ramps in each experiment?

      • Energy bar chart for Experiment 1: Ug bar is zero, Kt bar is 2 units, Kr bar is 1 unit. Energy bar chart for Experiment 2: Ug bar is zero, Kt bar is less than 2 units, Kr bar is less than 1 unit.
      • Energy bar chart for Experiment 1: Ug bar is zero, Kt bar is less than 2 units, Kr bar is less than 1 unit. Energy bar chart for Experiment 2: Ug bar is zero, Kt bar is 2 units, Kr bar is 1 unit.
      • Energy bar chart for Experiment 1: Ug bar is zero, Kt and Kr bars are both 1.5 units. Energy bar chart for Experiment 2: Ug bar is zero, Kt and Kr bars are both 1.5 units.
      • Energy bar chart for Experiment 1: Ug and Kt bars are both zero, Kr bar is 3 units. Energy bar chart for Experiment 2: Ug and Kr bars are both zero, Kt bar is 3 units.

      Choose your answer

      5
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      A slope with a sphere at the top on the left. The slope descends to a low point and rises again to a point labeled X.

      In an experiment, a solid sphere is released from the top of three tracks which are identical in size and shape, but have different coefficients of friction. In each trial, the sphere is released from rest at the same point and leaves the track at point X, as shown in the figure. In Trial 1, the sphere rolls without slipping along the entire track. In Trial 2, the sphere rolls and slips down the first slope and rolls without slipping up the next slope. In Trial 3, the sphere moves along a track with negligible friction. The maximum heights reached by each sphere after leaving the track are h subscript 1, h subscript 2, and h subscript 3 respectively.

      Which of the following correctly ranks h subscript 1, h subscript 2, and h subscript 3 from greatest to least?

      • h subscript 1 space greater than space h subscript 2 space greater than space h subscript 3

      • h subscript 3 space greater than space h subscript 2 space greater than space h subscript 1

      • h subscript 3 space greater than space h subscript 1 space greater than space h subscript 2

      • h subscript 2 space greater than space h subscript 1 space greater than space h subscript 3

      Choose your answer