PrepGo

AP Physics C: Mechanics Practice Quiz: Rotational Kinetic Energy

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

Test your understanding with short quizzes. This quiz has 9 questions to check your progress.

Question 1 of 9

Which of the following equations correctly represents the rotational kinetic energy, K_rot, of a rigid system with rotational inertia I and angular velocity ω?

All Questions (9)

Which of the following equations correctly represents the rotational kinetic energy, K_rot, of a rigid system with rotational inertia I and angular velocity ω?

A) K_rot = 1/2 Iω²

B) K_rot = Iω

C) K_rot = 1/2 mv²

D) K_rot = Iα

Correct Answer: A

Based on the provided content, the rotational kinetic energy of an object or rigid system is given by the equation K_rot = 1/2 Iω².

A flywheel is rotating with angular velocity ω and has a rotational kinetic energy K. If its angular velocity is doubled to 2ω while its rotational inertia remains constant, what is its new rotational kinetic energy?

A) 1/2 K

B) 2K

C) 4K

D) K

Correct Answer: C

Rotational kinetic energy is given by K_rot = 1/2 Iω². Since K is proportional to the square of the angular velocity (ω²), doubling the angular velocity results in a new kinetic energy of 1/2 I(2ω)² = 1/2 I(4ω²) = 4(1/2 Iω²) = 4K.

A solid sphere is rolling without slipping along a horizontal surface. Which of the following best describes the total kinetic energy of the sphere?

A) It consists solely of translational kinetic energy.

B) It consists solely of rotational kinetic energy.

C) It is the sum of its translational and rotational kinetic energies.

D) It is zero because the sphere is on a horizontal surface.

Correct Answer: C

The provided content states that the total kinetic energy of a rigid system is the sum of its rotational kinetic energy due to its rotation about its center of mass and the translational kinetic energy due to the linear motion of its center of mass. A rolling sphere has both types of motion.

Two wheels, A and B, are rotating with the same angular velocity. Wheel A has a rotational inertia that is three times the rotational inertia of Wheel B. What is the relationship between their rotational kinetic energies, K_A and K_B?

A) K_A = 1/3 K_B

B) K_A = K_B

C) K_A = 3K_B

D) K_A = 9K_B

Correct Answer: C

The formula for rotational kinetic energy is K_rot = 1/2 Iω². Since both wheels have the same angular velocity (ω), their kinetic energies are directly proportional to their rotational inertias (I). Given I_A = 3I_B, it follows that K_A = 1/2 (3I_B)ω² = 3(1/2 I_Bω²) = 3K_B.

A spinning top is rotating about a fixed point on the floor, but its center of mass is not moving horizontally or vertically. Which statement correctly describes the kinetic energy of the top?

A) The top has only translational kinetic energy.

B) The top has only rotational kinetic energy.

C) The top has both translational and rotational kinetic energy.

D) The top has no kinetic energy because its center of mass is stationary.

Correct Answer: B

Since the top's center of mass is not undergoing linear motion, its translational kinetic energy is zero. However, the top is rotating, so it possesses rotational kinetic energy. Therefore, its total kinetic energy is equal to its rotational kinetic energy.

The total kinetic energy of a rolling cylinder is 150 J. If its rotational kinetic energy is 50 J, what is its translational kinetic energy?

A) 50 J

B) 100 J

C) 150 J

D) 200 J

Correct Answer: B

The total kinetic energy of a rigid system is the sum of its translational and rotational kinetic energies (K_total = K_trans + K_rot). Given K_total = 150 J and K_rot = 50 J, the translational kinetic energy is K_trans = K_total - K_rot = 150 J - 50 J = 100 J.

Rotational kinetic energy is a function of which two physical quantities of a rigid system?

A) Mass and linear velocity

B) Force and radius

C) Torque and angular acceleration

D) Rotational inertia and angular velocity

Correct Answer: D

The provided content explicitly states that rotational kinetic energy is described in terms of the rotational inertia (I) and angular velocity (ω) of a rigid system, as shown in the formula K_rot = 1/2 Iω².

A rigid body is both rotating about its center of mass and translating through space. How would an observer calculate the body's total kinetic energy?

A) By calculating only its rotational kinetic energy.

B) By calculating only its translational kinetic energy.

C) By finding the sum of its rotational and translational kinetic energies.

D) By finding the product of its rotational and translational kinetic energies.

Correct Answer: C

According to the provided content, the total kinetic energy of a rigid system with both types of motion is the sum of its rotational kinetic energy (due to rotation about the center of mass) and its translational kinetic energy (due to the linear motion of the center of mass).

A solid disk and a hoop of the same mass and radius start from rest and roll without slipping down an incline. At the bottom, both have the same total kinetic energy. The hoop has a larger rotational inertia than the disk. Which statement correctly compares their rotational kinetic energies (K_rot) at the bottom?

A) The disk has more rotational kinetic energy.

B) The hoop has more rotational kinetic energy.

C) They have the same rotational kinetic energy.

D) The relationship cannot be determined without knowing their final velocities.

Correct Answer: B

This question requires synthesizing the concepts. Total kinetic energy is the sum of translational and rotational. For a rolling object, v = ωr. So K_total = 1/2 mv² + 1/2 Iω² = 1/2 mv² + 1/2 I(v/r)². The fraction of total energy that is rotational is dependent on I. Since the hoop has a larger rotational inertia (I), a larger fraction of its total kinetic energy will be in the form of rotational kinetic energy compared to the disk.