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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 6: Energy & Momentum of Rotating SystemsConservation of Angular Momentum

Conservation of Angular Momentum (College Board AP® Physics 1: Algebra-Based)

Exam Questions

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1
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Diagram of a swinging ball attached to a pole with a string, moving in a circular path. The radius of the circle is labeled r, and velocity is represented by v.

A tetherball is suspended from the top of a vertical stationary pole by a massless rope, as shown in the figure. The ball is given an initial speed vand the rope starts to wrap around the pole. The rotational inertia of the ball is I space equals space m r squared, where r is the distance between the ball and the pole.

Which of the following correctly represents the speed of the ball when the rope has become wrapped around the pole such that the distance between the ball and the pole has reduced by half?

  • 1 fourth v

  • 1 half v

  • 2 v

  • 4 v

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2
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A pottery wheel with a rotational inertia of 8.2 kg⋅m2 rotates at a constant rate of 22.0 rpm. The artist drops a lump of clay of mass 1.8 kg on the wheel, where it sticks at a distance of 46.0 cm from the axis of rotation.

If no net external torque acts on the system, which of the following is most nearly the angular speed of the wheel after the clay is dropped on it?

  • 2.1 space rad divided by straight s

  • 2.2 space rad divided by straight s

  • 2.3 space rad divided by straight s

  • 2.4 space rad divided by straight s

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3
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According to the accretion model of the Solar System, the planets formed from a slowly rotating nebula that collapsed under gravity.

Which of the following correctly describes why planets spin faster than the original nebula?

  • As the nebula collapses, the gravitational forces between the particles increase, causing the net torque on the nebula to increase

  • As the nebula collapses, the gravitational forces between the particles increase, increasing the angular momentum of the system

  • As the nebula collapses, the rotational inertia decreases, and the angular momentum remains constant

  • As the nebula collapses, the rotational inertia increases, causing an increase in angular acceleration

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4
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A spherical star of mass M and radius R rotates about its axis. It has a rotational inertia of 2 over 5 M R squared. The star explodes, ejecting mass in space radially and symmetrically. The remaining star is left with a mass of 1 over 10 M and a radius of 1 over 50 R.

What is the ratio of the star's final angular velocity to its initial angular velocity?

  • fraction numerator 1 over denominator 25 space 000 end fraction

  • 1 over 500

  • 500

  • 25 space 000

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5
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Diagram of a car driving on a circular track with radius r and speed v. Geometrical lines and angles are shown indicating distances from the track's center.

A circular track of mass M is placed on a massless horizontal ring which is free to rotate about a frictionless vertical axis, as shown in the figure. A battery-driven toy car of mass m is initially at rest on the track. As the car begins to move, it causes the track to rotate in the opposite direction. When the car moves with linear speed v, the angular speed of the ring is omega. The distance from the axis to the ring's outer edge is r and to the ring's inner edge is 3 over 5 r. The rotational inertia of the track-ring system is I space equals space 1 half M open parentheses r subscript 1 superscript 2 space plus space r subscript 2 superscript 2 close parentheses, where r subscript 1 is the inner radius and r subscript 2 is the outer radius.

Which of the following expressions correctly represents the angular speed of the ring omega?

  • fraction numerator 5 m v over denominator 8 M r end fraction

  • fraction numerator 15 m v over denominator 17 M r end fraction

  • fraction numerator 20 m v over denominator 17 M r end fraction

  • fraction numerator 25 m v over denominator 17 M r end fraction

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