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AP Physics C: Mechanics Practice Quiz: Conservation of Angular Momentum

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 13 questions to check your progress.

Question 1 of 13

What is the fundamental condition required for the total angular momentum of a rigid system to remain constant?

All Questions (13)

What is the fundamental condition required for the total angular momentum of a rigid system to remain constant?

A) The net external force on the system must be zero.

B) The net external torque on the system must be zero.

C) The rotational kinetic energy of the system must be constant.

D) The system's mass must be uniformly distributed.

Correct Answer: B

According to the provided content, 'If the net external torque exerted on a selected object or rigid system is zero, the total angular momentum of that system is constant.' A zero net external force ensures conservation of linear momentum, not necessarily angular momentum.

An ice skater is spinning with her arms extended. She then pulls her arms in close to her body. Assuming the friction from the ice provides a negligible torque, how does this action affect her angular momentum and rotational speed?

A) Her angular momentum increases, and her rotational speed increases.

B) Her angular momentum decreases, and her rotational speed increases.

C) Her angular momentum remains constant, and her rotational speed increases.

D) Her angular momentum remains constant, and her rotational speed decreases.

Correct Answer: C

Since the net external torque is zero, the skater's angular momentum is conserved. By pulling her arms in, she decreases her moment of inertia. To keep the angular momentum (product of moment of inertia and angular velocity) constant, her rotational speed must increase.

A child stands on the edge of a stationary merry-go-round. The child then starts to run clockwise around the edge. If the system is defined as the child and the merry-go-round, and there is no external torque, what will the merry-go-round do?

A) It will remain stationary.

B) It will rotate clockwise.

C) It will rotate counter-clockwise.

D) It will wobble but not rotate.

Correct Answer: C

The initial angular momentum of the child-merry-go-round system is zero. Since there is no net external torque, the total angular momentum must remain zero. When the child runs clockwise, they gain clockwise angular momentum. To conserve total angular momentum, the merry-go-round must gain an equal amount of counter-clockwise angular momentum, causing it to rotate counter-clockwise.

A planet orbits a star in a highly elliptical path. The gravitational force from the star on the planet is the only significant force acting. Why is the planet's angular momentum conserved throughout its orbit?

A) Because the planet's mass remains constant.

B) Because the gravitational force is always directed towards the star, producing zero torque about the star.

C) Because the planet's total mechanical energy is conserved.

D) Because the gravitational force is zero when the planet is farthest from the star.

Correct Answer: B

Torque is calculated as the cross product of the radius vector and the force vector. Since the gravitational force vector always points along the same line as the radius vector (from the planet to the star), the angle between them is 180 degrees, and the torque is zero. With zero net external torque, angular momentum is conserved.

Why is the selection of a system critical when applying the law of conservation of angular momentum?

A) Because angular momentum is only defined for isolated systems.

B) Because a force that is external to one system can be internal to a larger system.

C) Because larger systems always have more angular momentum.

D) Because the law only applies if the system's center of mass is stationary.

Correct Answer: B

The content states, 'Describe how the selection of a system determines whether the angular momentum of that system changes.' A torque is caused by an external force. If you expand your system to include the object exerting that force, the interaction becomes an internal force pair, which does not produce a net torque on the larger system.

According to the provided principles, a change in a system's total angular momentum must be caused by which of the following?

A) A redistribution of mass within the system.

B) An interaction between the system and its surroundings.

C) A change in the system's rotational kinetic energy.

D) Forces acting between components within the system.

Correct Answer: B

This is a direct application of the principle: 'Any change to a system’s angular momentum must be due to an interaction between the system and its surroundings.' This interaction manifests as a net external torque.

A spinning disk is dropped onto an identical, non-spinning disk, and they stick together. If the system is defined as *only the top disk*, is its angular momentum conserved during the interaction?

A) Yes, because its mass does not change.

B) Yes, because gravity is the only external force.

C) No, because the bottom disk exerts a frictional torque on it.

D) No, because its rotational kinetic energy is not conserved.

Correct Answer: C

When considering only the top disk as the system, the frictional force from the bottom disk is an external force that creates a torque, slowing its rotation. This net external torque changes the angular momentum of the top disk.

Following the previous scenario, a spinning disk is dropped onto an identical, non-spinning disk, and they stick together. If the system is now defined as *both disks together*, is the total angular momentum of this system conserved?

A) No, because the collision is inelastic and kinetic energy is lost.

B) No, because the final angular velocity is less than the initial angular velocity.

C) Yes, because the torques the disks exert on each other are internal to the system.

D) It depends on whether the disks are dropped in a vacuum.

Correct Answer: C

When the system includes both disks, the frictional torques they exert on each other are internal. These are an action-reaction pair and cancel out, resulting in no net torque on the two-disk system (assuming no external torque from the axle). Therefore, the total angular momentum of the two-disk system is conserved.

A diver jumps from a diving board, pulls into a tuck to spin rapidly, and then straightens out before entering the water. The primary reason their spin rate increases in the tuck position is that:

A) The torque from gravity increases in the tuck position.

B) Their angular momentum is conserved, and their moment of inertia decreases.

C) They push off the air to generate more angular momentum.

D) Their angular momentum increases as their potential energy decreases.

Correct Answer: B

Assuming air resistance is negligible, the only external force is gravity, which acts on the diver's center of mass and produces no torque. Thus, the diver's angular momentum is conserved. By pulling into a tuck, the diver reduces their moment of inertia, which causes their angular velocity to increase to conserve angular momentum (L = Iω).

If the total angular momentum of a system is observed to be constant, which of the following statements must be true based on the provided principles?

A) The system is not rotating.

B) The system's angular velocity is constant.

C) The net external torque on the system is zero.

D) The system's moment of inertia is constant.

Correct Answer: C

The conservation of angular momentum is a direct consequence of the net external torque on the system being zero. The angular velocity and moment of inertia can both change (as in the ice skater example), as long as their product, the angular momentum, remains constant.

A student sits at rest on a stool that can rotate freely. They are holding a bicycle wheel that is spinning counter-clockwise when viewed from above. The student then flips the wheel over 180 degrees. What is the resulting motion of the student and the stool?

A) They remain at rest.

B) They begin to rotate clockwise.

C) They begin to rotate counter-clockwise.

D) They oscillate back and forth briefly and then stop.

Correct Answer: C

The system is the student, stool, and wheel. Initially, the total angular momentum is that of the wheel (let's call it +L). When the wheel is flipped, its angular momentum becomes -L. To conserve the total angular momentum of the system at its initial value of +L, the student and stool must gain an angular momentum of +2L. Therefore, they will begin to rotate counter-clockwise.

Which of the following scenarios is best described by the conservation of linear momentum, rather than the conservation of angular momentum?

A) A planet moving faster in its orbit when it is closer to its star.

B) A rocket engine firing in deep space, causing the rocket to accelerate.

C) A spinning figure skater pulling their arms in to spin faster.

D) A collapsing star spinning more rapidly as its radius decreases.

Correct Answer: B

A rocket's acceleration is due to the expulsion of mass (exhaust gas). The total linear momentum of the system (rocket + gas) is conserved. The other options are all classic examples of conservation of angular momentum, where a change in moment of inertia leads to a change in angular velocity.

A massive star undergoes a supernova explosion and collapses into a much smaller, denser neutron star. Assuming the system does not lose mass and the net external torque is zero, how do the final angular momentum (L_f) and final angular velocity (ω_f) compare to the initial values (L_i and ω_i)?

A) L_f = L_i and ω_f < ω_i

B) L_f > L_i and ω_f > ω_i

C) L_f < L_i and ω_f = ω_i

D) L_f = L_i and ω_f > ω_i

Correct Answer: D

Since the net external torque on the star is zero, its angular momentum is conserved (L_f = L_i). The collapse dramatically decreases the star's radius and therefore its moment of inertia (I). Because angular momentum (L = Iω) is conserved, a large decrease in I must be compensated by a large increase in angular velocity (ω) to keep the product constant.