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AP Physics C: Mechanics 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 14 questions to check your progress.

Question 1 of 14

Which equation correctly describes the magnitude of the angular momentum of a rigid system, such as a spinning flywheel, rotating about a specific axis?

All Questions (14)

Which equation correctly describes the magnitude of the angular momentum of a rigid system, such as a spinning flywheel, rotating about a specific axis?

A) L = Iω

B) L = r × p

C) L = ∫τ dt

D) L = mvr

Correct Answer: A

The provided content explicitly states that 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 rotational inertia and ω is the angular velocity.

The angular momentum of a single object, such as a planet orbiting a star, about a given point is defined by which vector expression?

A) The dot product of its position vector and its linear momentum.

B) The sum of its rotational inertia and its angular velocity.

C) The cross product of its position vector and its linear momentum.

D) The integral of the torque acting on it over time.

Correct Answer: C

The content provides the equation L⃗=r⃗×p⃗ for the angular momentum of an object about a given point. This represents the cross product of the position vector (r) and the linear momentum vector (p).

How is angular impulse defined?

A) The product of a system's rotational inertia and its change in angular velocity.

B) The derivative of angular momentum with respect to time.

C) The integral of the torque exerted on a system over a time interval.

D) The cross product of the lever arm and the applied force.

Correct Answer: C

The content directly defines angular impulse as the integral of the torque exerted on an object or rigid system over a time interval, given by the equation: angular impulse = ∫τ⃗ dt.

A rigid spinning top has a rotational inertia I and an angular velocity ω. If its angular velocity is tripled while its rotational inertia remains constant, how does the magnitude of its angular momentum, L, change?

A) L is reduced to one-third its original value.

B) L remains the same.

C) L is tripled.

D) L increases by a factor of nine.

Correct Answer: C

According to the equation L = Iω, angular momentum is directly proportional to angular velocity. If ω is tripled and I is constant, the new angular momentum L' = I(3ω) = 3(Iω) = 3L.

A moving particle has linear momentum p⃗ and is at a position r⃗ relative to an origin. The magnitude of its angular momentum about the origin is calculated to be zero. Which statement must be true about the particle's motion?

A) The particle's velocity vector points directly toward or away from the origin.

B) The particle's velocity vector is perpendicular to its position vector.

C) The particle is moving in a uniform circle about the origin.

D) The particle is momentarily at rest.

Correct Answer: A

The angular momentum is given by L⃗=r⃗×p⃗. The magnitude of this cross product is zero if the vectors r⃗ and p⃗ are parallel or anti-parallel. Since p⃗ has the same direction as the velocity vector, this means the particle's line of motion passes through the origin.

A variable torque is applied to a rigid body. If this torque is plotted as a function of time, what physical quantity is represented by the area under the curve over a specific time interval?

A) The change in angular momentum.

B) The average angular velocity.

C) The total work done by the torque.

D) The angular impulse delivered.

Correct Answer: D

The definition of angular impulse is the integral of torque over a time interval: ∫τ⃗ dt. A definite integral mathematically represents the area under the curve of the function. Therefore, the area under the torque-time graph is the angular impulse.

In the equation L = Iω for a rigid system, what does the variable ω represent?

A) Work

B) Weight

C) Angular velocity

D) Rotational inertia

Correct Answer: C

In the standard equation for the angular momentum of a rigid body, L = Iω, L is the angular momentum, I is the rotational inertia, and ω is the angular velocity.

A student is asked to compare the angular momentum of a spinning, uniform solid sphere about its center with the angular momentum of a small satellite orbiting a distant planet. Which pair of equations is most appropriate for these two scenarios, respectively?

A) L = Iω for the sphere, and L⃗=r⃗×p⃗ for the satellite.

B) L⃗=r⃗×p⃗ for the sphere, and L = Iω for the satellite.

C) L = Iω for both.

D) L⃗=r⃗×p⃗ for both.

Correct Answer: A

The spinning sphere is a rigid system rotating about a specific axis (its center), so L = Iω is appropriate. The satellite is best treated as a single object moving about a given point (the planet), making L⃗=r⃗×p⃗ the appropriate choice.

A constant torque τ₀ is applied to a merry-go-round for a time interval Δt. Which of the following expressions represents the angular impulse delivered during this interval?

A) τ₀ / Δt

B) τ₀

C) 0.5 * τ₀ * (Δt)²

D) τ₀ * Δt

Correct Answer: D

Angular impulse is the integral of torque over time. For a constant torque τ₀, the integral ∫τ₀ dt becomes τ₀ ∫dt = τ₀[t] evaluated over the interval Δt, which simplifies to τ₀ * Δt.

Based on the equation L⃗=r⃗×p⃗, what are the fundamental SI units for angular momentum?

A) kg⋅m/s

B) kg⋅m²/s

C) kg⋅m/s²

D) N⋅m

Correct Answer: B

The position vector r⃗ has units of meters (m). The linear momentum p⃗ (mass × velocity) has units of kg⋅(m/s). The product of these units is m ⋅ (kg⋅m/s), which simplifies to kg⋅m²/s.

Based on its definition as the integral of torque over a time interval, what are the SI units for angular impulse?

A) N/s

B) N⋅m

C) N⋅s

D) N⋅m⋅s

Correct Answer: D

The definition is angular impulse = ∫τ⃗ dt. The SI unit for torque (τ) is the Newton-meter (N⋅m). The SI unit for time (t) is the second (s). Therefore, the unit for angular impulse is the product, N⋅m⋅s.

A spinning disk has angular momentum L. A second disk is constructed with half the rotational inertia but is spun at four times the angular velocity. What is the angular momentum of the second disk?

A) L/2

B) L

C) 2L

D) 4L

Correct Answer: C

The initial angular momentum is L = Iω. The new rotational inertia is I' = I/2 and the new angular velocity is ω' = 4ω. The new angular momentum is L' = I'ω' = (I/2)(4ω) = 2(Iω) = 2L.

To calculate the angular momentum of a particle about a specific point using the equation L⃗=r⃗×p⃗, which set of quantities is required?

A) The particle's mass, angular velocity, and radius of motion.

B) The torque on the particle, the time interval, and its rotational inertia.

C) The particle's mass, its velocity vector, and its position vector relative to the point.

D) The particle's rotational inertia and its angular acceleration.

Correct Answer: C

The equation L⃗=r⃗×p⃗ directly involves the position vector r⃗ and the linear momentum vector p⃗. To find p⃗, one needs the particle's mass (m) and its velocity vector (v⃗), since p⃗=mv⃗. Therefore, mass, velocity vector, and position vector are all required.

An object is subjected to a time-varying net torque. If the total angular impulse delivered to the object over a 10-second interval is zero, what must be true?

A) The net torque was zero for the entire 10-second interval.

B) The object's angular velocity was constant for the interval.

C) The net area under the torque-versus-time graph for that interval is zero.

D) The torque was positive for the first 5 seconds and negative for the last 5 seconds.

Correct Answer: C

Angular impulse is the integral of torque over time, which is equivalent to the net area under the torque-time graph. A total angular impulse of zero means this net area must be zero. This can happen if the torque is always zero, or if positive and negative torques are applied such that the positive and negative areas cancel out.