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AP Physics 1: Algebra-Based 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 14 questions to check your progress.

Question 1 of 14

Under which of the following conditions is the total angular momentum of a system guaranteed to be constant?

All Questions (14)

Under which of the following conditions is the total angular momentum of a system guaranteed to be constant?

A) The net external force on the system is zero.

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

C) The system's rotational inertia is constant.

D) The system's angular velocity is constant.

Correct Answer: B

Based on 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.' The other conditions are not sufficient to guarantee conservation of angular momentum.

An ice skater is spinning with their arms extended. They then pull their arms in close to their body. Assuming no net external torque acts on the skater, how does this action affect their angular momentum and angular velocity?

A) Angular momentum increases; angular velocity increases.

B) Angular momentum decreases; angular velocity remains constant.

C) Angular momentum remains constant; angular velocity increases.

D) Angular momentum remains constant; angular velocity decreases.

Correct Answer: C

Since there is no net external torque, the skater's angular momentum is conserved and remains constant. By pulling their arms in, they decrease their rotational inertia. To keep angular momentum constant, their angular velocity must increase. This describes the behavior of the system using conservation of angular momentum.

According to the provided principles, which statement best describes the conservation of angular momentum?

A) It is a principle that applies only to rigid, solid objects.

B) It is conserved only when linear momentum is also conserved.

C) It is conserved in all interactions.

D) It is only conserved in the absence of gravity.

Correct Answer: C

The provided content explicitly states, 'Angular momentum is conserved in all interactions.' This implies it is a fundamental conservation law applicable across all interactions within a closed system.

A student sits on a spinning stool holding a spinning bicycle wheel. The student then flips the wheel upside down. If the 'system' is defined as only the student and the stool (excluding the wheel), what can be said about the angular momentum of this system?

A) The angular momentum of the system is constant because there are no external torques.

B) The angular momentum of the system changes because the wheel exerts a torque on the student.

C) The angular momentum of the system is zero.

D) The angular momentum of the system is constant because the student's mass does not change.

Correct Answer: B

The selection of the system is crucial. Since the system is defined as only the student and the stool, the wheel is external. When the student flips the wheel, the wheel exerts a torque on the student. This is an external torque on the selected system, which changes the angular momentum of the student-stool system.

Reconsidering the scenario of a student on a spinning stool holding a spinning bicycle wheel, if the 'system' is now defined as the student, the stool, AND the wheel, what happens to the total angular momentum of this new system when the student flips the wheel?

A) The total angular momentum changes because the wheel's orientation is reversed.

B) The total angular momentum changes because the student does work.

C) The total angular momentum remains constant because the torque the student exerts on the wheel is internal to the system.

D) The total angular momentum becomes zero.

Correct Answer: C

When the system includes the student, stool, and wheel, the torque the student exerts on the wheel and the equal-and-opposite torque the wheel exerts on the student are internal torques. Assuming no net external torque, the total angular momentum of this complete system is constant. This illustrates how the selection of the system determines whether angular momentum is conserved.

A system consists of two disks mounted on the same frictionless axle. Disk A is spinning with angular momentum L_A, and Disk B is initially at rest. Disk A is then dropped onto Disk B, and they stick together. What is the total angular momentum of the two-disk system immediately after they stick together?

A) L_A

B) L_A / 2

C) 2 * L_A

D) 0

Correct Answer: A

The total angular momentum of a system is the sum of the angular momenta of its parts. Before the collision, the total angular momentum was L_A + 0 = L_A. Since the torques during the collision are internal to the two-disk system, the net external torque is zero. Therefore, the total angular momentum of the system is conserved and remains L_A after the collision.

A spinning top is rotating on a frictionless surface. A small puff of air exerts a brief force on the side of the top, away from its axis of rotation. What is the effect of this puff of air on the top's angular momentum?

A) The angular momentum remains constant because the force was brief.

B) The angular momentum remains constant because the surface is frictionless.

C) The angular momentum changes because the puff of air exerted a net external torque.

D) The angular momentum becomes zero.

Correct Answer: C

The puff of air exerts an external force at a distance from the axis of rotation, creating a net external torque. According to the principle, if the net external torque is not zero, the total angular momentum of the system is not constant. Therefore, the angular momentum changes.

A planet orbits a star in a highly elliptical path. As the planet moves from its farthest point to its closest point, what happens to the angular momentum of the planet-star system?

A) It increases because the planet's speed increases.

B) It decreases because the distance to the star decreases.

C) It remains constant because the gravitational force exerts no torque about the star.

D) It changes direction but not magnitude.

Correct Answer: C

The gravitational force exerted by the star on the planet is always directed towards the star. When considering the star as the axis of rotation, this force has a lever arm of zero, meaning it exerts no torque on the planet. With zero net external torque, the angular momentum of the planet-star system is conserved and remains constant.

A rigid system is composed of three particles, all rotating about the same central axis. The individual angular momenta of the particles about this axis are L1, L2, and L3. How is the total angular momentum, L_total, of the system calculated?

A) L_total = (L1 + L2 + L3) / 3

B) L_total = L1 + L2 + L3

C) L_total = The largest of L1, L2, or L3

D) L_total = L1 * L2 * L3

Correct Answer: B

This question directly tests the principle that 'The total angular momentum of a system about a rotational axis is the sum of the angular momenta of the system’s constituent parts about that axis.'

A diver jumps from a diving board and goes into a tight tuck position. They then open up into a straight layout position just before entering the water. Which of the following correctly describes the change in their rotational inertia and angular velocity from the tuck to the layout position, assuming angular momentum is conserved?

A) Rotational inertia increases; angular velocity increases.

B) Rotational inertia decreases; angular velocity increases.

C) Rotational inertia increases; angular velocity decreases.

D) Rotational inertia decreases; angular velocity decreases.

Correct Answer: C

Moving from a tight tuck to a straight layout increases the diver's rotational inertia (I). Because angular momentum (L) is conserved in the absence of external torques, an increase in I must be accompanied by a decrease in angular velocity (ω). This is an application of describing system behavior using conservation of angular momentum.

What is the direct consequence for a system if the net external torque exerted on it is zero?

A) The system's angular velocity must be zero.

B) The system's rotational inertia must be zero.

C) The system's total angular momentum is constant.

D) The system must stop rotating.

Correct Answer: C

This is a direct restatement of the principle: '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 horizontal platform is rotating freely. A person stands at the center. The person then walks out towards the edge of the platform. If the person and platform are considered a single system, which statement is correct?

A) The angular momentum of the platform decreases, but the total angular momentum of the system remains constant.

B) The angular momentum of the person remains zero, and the angular momentum of the platform remains constant.

C) The total angular momentum of the system increases because the person is moving.

D) The total angular momentum of the system decreases because of the friction from the person walking.

Correct Answer: A

The person and platform form a system with no net external torque, so total angular momentum is conserved. As the person walks outward, the system's total rotational inertia increases, causing the system's angular velocity to decrease. The total angular momentum is the sum of the person's and the platform's angular momenta. As the person gains angular momentum, the platform must lose angular momentum (by slowing down) to keep the total sum constant.

The statement 'Angular momentum is conserved in all interactions' is a fundamental principle. This conservation is conditional upon what?

A) The interaction occurring in a vacuum.

B) The absence of a net external torque on the system.

C) The masses of the interacting objects being equal.

D) The interaction being perfectly elastic.

Correct Answer: B

While the provided content states 'Angular momentum is conserved in all interactions,' it qualifies this with the condition: 'If the net external torque exerted on a selected object or rigid system is zero, the total angular momentum of that system is constant.' This condition is the key to applying the conservation law.

A child is playing on a merry-go-round that is rotating. The child, initially at the edge, walks toward the center. What is the effect on the merry-go-round's rotational speed?

A) It decreases because the child's mass is now closer to the center.

B) It remains the same because the child's mass has not changed.

C) It increases because the total rotational inertia of the system has decreased.

D) It increases because the child exerts a forward force on the merry-go-round.

Correct Answer: C

Considering the child and merry-go-round as a system, there is no net external torque, so the system's angular momentum is conserved. When the child walks toward the center, the system's total rotational inertia (I) decreases. To keep the angular momentum (L) constant, the angular velocity (ω), or rotational speed, of the system must increase.