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
All Questions (14)
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.
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).
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) 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) 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) 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.
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) 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) 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.
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.
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) 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.
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.
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.