AP Physics 1: Algebra-Based Practice Quiz: Angular Momentum and Angular Impulse

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

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

Which of the following best describes angular impulse?

A)The product of an object's moment of inertia and its angular velocity.B)The product of the average torque exerted on an object and the time interval over which it is exerted.C)The rate of change of angular momentum.D)The rotational equivalent of kinetic energy.

All Questions (16)

Which of the following best describes angular impulse?

A) The product of an object's moment of inertia and its angular velocity.

B) The product of the average torque exerted on an object and the time interval over which it is exerted.

C) The rate of change of angular momentum.

D) The rotational equivalent of kinetic energy.

Correct Answer: B

Based on the provided content, 'Angular impulse is defined as the product of the torque exerted on an object or rigid system and the time interval during which the torque is exerted: angular impulse = τ_avg Δt'.

For a rigid system rotating about a specific axis, its angular momentum (L) is described by which equation?

A) L = r⊥mv

B) L = τ_avg Δt

C) L = Iω

D) L = rmv sinθ

Correct Answer: C

The content states, 'The magnitude of the angular momentum of a rigid system about a specific axis can be described with the equation: L = Iω', where I is the moment of inertia and ω is the angular velocity.

What is the fundamental relationship between the change in angular momentum (ΔL) of a system and the angular impulse delivered to it?

A) The angular impulse is the initial angular momentum divided by the time interval.

B) The change in angular momentum is inversely proportional to the angular impulse.

C) The change in angular momentum is equal to the angular impulse exerted on the system.

D) The angular impulse is equal to the final angular momentum of the system.

Correct Answer: C

The provided content explicitly states: 'The angular impulse exerted on an object or rigid system is equal to the change in angular momentum of that object or rigid system: ΔL = angular impulse'.

A spinning flywheel with a moment of inertia of 10 kg·m² has an angular velocity of 5 rad/s. What is the magnitude of its angular momentum?

A) 2 kg·m²/s

B) 15 kg·m²/s

C) 50 kg·m²/s

D) 0.5 kg·m²/s

Correct Answer: C

Using the formula for the angular momentum of a rigid system, L = Iω. Given I = 10 kg·m² and ω = 5 rad/s, L = (10 kg·m²)(5 rad/s) = 50 kg·m²/s.

A 2 kg object moves at a constant velocity of 5 m/s. What is the magnitude of its angular momentum about a point that is 3 m away from the object's path of motion, measured perpendicularly?

A) 10 kg·m²/s

B) 15 kg·m²/s

C) 30 kg·m²/s

D) 60 kg·m²/s

Correct Answer: C

The magnitude of the angular momentum of an object about a point is given by L = r⊥mv. Here, r⊥ = 3 m, m = 2 kg, and v = 5 m/s. Therefore, L = (3 m)(2 kg)(5 m/s) = 30 kg·m²/s.

An average torque of 20 N·m is applied to a spinning top for 0.5 seconds. What is the magnitude of the angular impulse delivered to the top?

A) 10 N·m·s

B) 20 N·m·s

C) 40 N·m·s

D) 100 N·m·s

Correct Answer: A

Angular impulse is calculated as the product of the average torque and the time interval: angular impulse = τ_avg Δt. Given τ_avg = 20 N·m and Δt = 0.5 s, the angular impulse is (20 N·m)(0.5 s) = 10 N·m·s.

A rigid body, initially at rest, is subjected to a net torque. According to the principles of angular impulse and angular momentum, what must be true?

A) The body's final angular momentum is zero.

B) The body's moment of inertia will decrease.

C) The body will experience a change in angular momentum.

D) The body will not rotate.

Correct Answer: C

An angular impulse (τ_avg Δt) is delivered by the net torque. The content states that the angular impulse is equal to the change in angular momentum (ΔL). Since the body starts from rest (initial L = 0) and receives an angular impulse, its angular momentum must change, resulting in a non-zero final angular momentum.

A 0.5 kg ball is swung in a circle on a 2 m long string. At a certain instant, the ball has a speed of 6 m/s. The angle between the string (radius vector) and the velocity vector is 90°. What is the magnitude of the ball's angular momentum about the center of the circle?

A) 3 kg·m²/s

B) 6 kg·m²/s

C) 12 kg·m²/s

D) 24 kg·m²/s

Correct Answer: B

The angular momentum of an object about a point is L = rmv sinθ. Here, r = 2 m, m = 0.5 kg, v = 6 m/s, and θ = 90°. Since sin(90°) = 1, the formula simplifies to L = rmv. L = (2 m)(0.5 kg)(6 m/s) = 6 kg·m²/s.

A spinning disk has its angular velocity doubled while its moment of inertia remains constant. How does its angular momentum change?

A) It is halved.

B) It remains the same.

C) It is doubled.

D) It is quadrupled.

Correct Answer: C

The angular momentum of a rigid system is given by L = Iω. If the moment of inertia (I) is constant and the angular velocity (ω) is doubled, the new angular momentum L' = I(2ω) = 2(Iω) = 2L. Therefore, the angular momentum is doubled.

A merry-go-round with a moment of inertia of 500 kg·m² is initially at rest. A constant torque is applied for 10 seconds, causing its angular momentum to increase to 2000 kg·m²/s. What was the magnitude of the applied torque?

A) 20 N·m

B) 50 N·m

C) 200 N·m

D) 5000 N·m

Correct Answer: C

The relationship is ΔL = τ_avg Δt. The change in angular momentum ΔL is L_final - L_initial = 2000 kg·m²/s - 0 = 2000 kg·m²/s. The time interval Δt is 10 s. Rearranging the formula to solve for torque: τ_avg = ΔL / Δt = 2000 kg·m²/s / 10 s = 200 N·m.

A particle of mass m moves with velocity v. The magnitude of its angular momentum about a point P is given by L = rmv sinθ. What does θ represent in this equation?

A) The angle between the position vector and the acceleration vector.

B) The angle between the position vector and the momentum vector.

C) The angle of the particle's trajectory relative to the horizontal.

D) The angle between the force vector and the position vector.

Correct Answer: B

In the equation L = rmv sinθ, r is the magnitude of the position vector from the point P to the particle, mv is the magnitude of the linear momentum, and θ is the angle between the position vector and the linear momentum (or velocity) vector. This is explicitly stated in the provided content.

A disk with a moment of inertia of 2 kg·m² is spinning at 4 rad/s. A frictional torque of -0.5 N·m is applied. How long does it take for the disk to come to a complete stop?

A) 4 s

B) 8 s

C) 16 s

D) 32 s

Correct Answer: C

First, calculate the initial angular momentum: L_initial = Iω = (2 kg·m²)(4 rad/s) = 8 kg·m²/s. The final angular momentum is L_final = 0. The change in angular momentum is ΔL = L_final - L_initial = -8 kg·m²/s. We know ΔL = τ Δt. So, -8 kg·m²/s = (-0.5 N·m) Δt. Solving for Δt gives Δt = (-8) / (-0.5) = 16 s.

Which of the following quantities causes a change in the angular momentum of a rigid system?

A) A constant angular velocity.

B) An internal force between parts of the system.

C) An angular impulse.

D) The system's moment of inertia.

Correct Answer: C

The content establishes the direct relationship: 'The angular impulse exerted on an object or rigid system is equal to the change in angular momentum of that object or rigid system'. Therefore, an angular impulse is what causes the change.

A 1 kg particle is located at position r = (3i + 4j) m and moves with a velocity v = 5i m/s. What is the magnitude of its angular momentum about the origin using the formula L = rmv sinθ?

A) 0 kg·m²/s

B) 15 kg·m²/s

C) 20 kg·m²/s

D) 25 kg·m²/s

Correct Answer: C

The formula L = r⊥mv is easiest here. The velocity is purely in the x-direction. The perpendicular distance (r⊥) from the origin to the line of motion (the x-axis) is the y-component of the position vector, which is 4 m. So, L = r⊥mv = (4 m)(1 kg)(5 m/s) = 20 kg·m²/s. Alternatively, using L = rmv sinθ, the magnitude of r is sqrt(3²+4²) = 5 m. The angle θ is the angle between r and v. sinθ = (y-component of r) / (magnitude of r) = 4/5. So L = (5 m)(1 kg)(5 m/s)(4/5) = 20 kg·m²/s.

If a net torque is applied to an object that is already rotating, the object's angular momentum will change. This change is equal to the:

A) final angular velocity.

B) moment of inertia.

C) angular impulse provided by the torque.

D) work done by the torque.

Correct Answer: C

This is a direct application of the angular impulse-momentum theorem. The content states, 'Relate the change in angular momentum of an object or rigid system to the angular impulse given to that object or rigid system' and 'ΔL = angular impulse'.

A child applies a tangential force of 10 N to the edge of a merry-go-round of radius 2 m for 3 seconds. If the merry-go-round was initially at rest and has a moment of inertia of 150 kg·m², what is its final angular velocity?

A) 0.2 rad/s

B) 0.4 rad/s

C) 0.6 rad/s

D) 0.8 rad/s

Correct Answer: B

First, find the torque: τ = rF = (2 m)(10 N) = 20 N·m. Next, find the angular impulse: impulse = τΔt = (20 N·m)(3 s) = 60 N·m·s. This impulse equals the change in angular momentum: ΔL = 60 kg·m²/s. Since it started from rest, ΔL = L_final = Iω_final. So, 60 kg·m²/s = (150 kg·m²)ω_final. Solving for ω_final gives ω_final = 60 / 150 = 0.4 rad/s.