AP Physics C: Mechanics Practice Quiz: Rolling

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

According to the provided content, the total kinetic energy of a system that is rolling is described as the sum of which two types of energy?

A)Potential and RotationalB)Translational and RotationalC)Translational and PotentialD)Frictional and Translational

All Questions (14)

According to the provided content, the total kinetic energy of a system that is rolling is described as the sum of which two types of energy?

A) Potential and Rotational

B) Translational and Rotational

C) Translational and Potential

D) Frictional and Translational

Correct Answer: B

The content explicitly states that the total kinetic energy of a system is the sum of the system’s translational and rotational kinetic energies, represented by the equation $K_{tot}=K_{trans}+K_{rot}$.

Which equation correctly relates the translational speed of a system's center of mass ($v_{cm}$) to its angular speed (ω) when it is rolling without slipping?

A) $v_{cm} = r / \omega$

B) $v_{cm} = \omega / r$

C) $v_{cm} = r\omega$

D) $v_{cm} = r\omega^2$

Correct Answer: C

The provided content gives the direct relationship for rolling without slipping as $v_{cm}=r\omega$, where r is the radius of the rolling object.

In an ideal case of a sphere rolling without slipping down a ramp, what is the role of the frictional force regarding the system's energy?

A) It converts kinetic energy into thermal energy.

B) It increases the total mechanical energy of the system.

C) It does not dissipate any energy from the system.

D) It is the primary source of energy dissipation.

Correct Answer: C

The content states that for ideal cases, rolling without slipping implies that the frictional force does not dissipate any energy from the rolling system. This static friction provides the torque for rotation but does no work.

A wheel with a radius of 0.5 m rolls without slipping. If its center of mass travels a distance of 3.0 m, what is the total angle in radians through which the wheel has rotated?

A) 1.5 rad

B) 3.0 rad

C) 3.5 rad

D) 6.0 rad

Correct Answer: D

The relationship between the displacement of the center of mass and the angle of rotation is $\Delta x_{cm}=r\Delta\theta$. Rearranging for the angle gives $\Delta\theta = \Delta x_{cm} / r$. Plugging in the values: $\Delta\theta = 3.0 \text{ m} / 0.5 \text{ m} = 6.0 \text{ rad}$.

What is the fundamental characteristic of a system's motion when it is described as 'rolling without slipping'?

A) The system has only rotational motion.

B) The system's translational and rotational motions are unrelated.

C) The system's translational motion is directly related to its rotational motion.

D) The system experiences no frictional force.

Correct Answer: C

The content specifies that while rolling without slipping, the translational motion of the system's center of mass is related to the rotational motion of the system itself through a set of specific equations ($v_{cm}=r\omega$, etc.).

Which of the following equations represents the total kinetic energy ($K_{tot}$) of a system that has both translational and rotational motion?

A) $K_{tot}=K_{trans} - K_{rot}$

B) $K_{tot}=K_{trans} / K_{rot}$

C) $K_{tot}=K_{rot} - K_{trans}$

D) $K_{tot}=K_{trans} + K_{rot}$

Correct Answer: D

The content provides the exact equation for the total kinetic energy of such a system: $K_{tot}=K_{trans}+K_{rot}$.

A cylinder is rolling without slipping and its center of mass is accelerating at a rate of $a_{cm}$. If the cylinder's radius is *r*, what is its angular acceleration, $\alpha$?

A) $\alpha = a_{cm} / r$

B) $\alpha = a_{cm} \cdot r$

C) $\alpha = r / a_{cm}$

D) $\alpha = a_{cm} / r^2$

Correct Answer: A

The provided content gives the relationship between the linear acceleration of the center of mass and the angular acceleration for an object rolling without slipping as $a_{cm}=r\alpha$. To find the angular acceleration, we rearrange the formula to $\alpha = a_{cm} / r$.

A rolling object's motion can be described as a combination of what two fundamental types of motion?

A) Translational and rotational

B) Vibrational and rotational

C) Circular and potential

D) Translational and oscillatory

Correct Answer: A

The first point of the provided content states that the kinetic energy of a rolling system is due to its translational and rotational motion, which are the two components of its overall motion.

A bowling ball with a radius of 11 cm is thrown down a lane. It is rolling without slipping with a center of mass speed of 8 m/s. What is its approximate angular speed?

A) 0.88 rad/s

B) 13.75 rad/s

C) 72.7 rad/s

D) 88 rad/s

Correct Answer: C

Using the equation $v_{cm}=r\omega$ and solving for $\omega$, we get $\omega = v_{cm}/r$. It is critical to convert the radius from cm to m: $r = 11 \text{ cm} = 0.11 \text{ m}$. Therefore, $\omega = 8 \text{ m/s} / 0.11 \text{ m} \approx 72.7 \text{ rad/s}$.

The condition that the frictional force does not dissipate energy from a rolling system is specified for which scenario?

A) When the system is slipping and sliding.

B) In all situations involving friction.

C) For ideal cases of rolling without slipping.

D) Only for objects rolling on a frictionless surface.

Correct Answer: C

The content explicitly states, 'For ideal cases, rolling without slipping implies that the frictional force does not dissipate any energy from the rolling system.'

A car tire accelerates from rest without slipping. Its angular acceleration is a constant 10 rad/s². If the tire's radius is 0.4 m, what is the linear acceleration of the car?

A) 0.04 m/s²

B) 4.0 m/s²

C) 25 m/s²

D) 40 m/s²

Correct Answer: B

The linear acceleration of the center of mass is related to the angular acceleration by the equation $a_{cm}=r\alpha$. Using the given values: $a_{cm} = (0.4 \text{ m})(10 \text{ rad/s}^2) = 4.0 \text{ m/s}^2$.

If a rolling system's total kinetic energy is given by $K_{tot}$, its translational kinetic energy is $K_{trans}$, and its rotational kinetic energy is $K_{rot}$, which statement is always true for an object that is rolling?

A) $K_{tot}$ is always less than $K_{trans}$.

B) $K_{tot}$ is always equal to $K_{rot}$.

C) $K_{tot}$ is always greater than $K_{trans}$.

D) $K_{trans}$ is always equal to $K_{rot}$.

Correct Answer: C

The total kinetic energy is the sum $K_{tot}=K_{trans}+K_{rot}$. Since an object that is rolling has both translational and rotational motion, $K_{rot}$ must be a positive value. Therefore, the total kinetic energy must be greater than the translational kinetic energy alone.

The set of equations $\Delta x_{cm}=r\Delta\theta$, $v_{cm}=r\omega$, and $a_{cm}=r\alpha$ are valid under what specific condition of motion?

A) Pure translational motion

B) Rolling with slipping

C) Pure rotational motion

D) Rolling without slipping

Correct Answer: D

The provided content explicitly lists these equations as the relationships that define the motion of a system that is rolling without slipping.

A bicycle wheel of radius *r* rotates through an angle $\Delta\theta$ as it rolls without slipping. Which expression represents the distance $\Delta x_{cm}$ the center of the wheel has traveled?

A) $\Delta x_{cm} = \Delta\theta / r$

B) $\Delta x_{cm} = r / \Delta\theta$

C) $\Delta x_{cm} = r\Delta\theta$

D) $\Delta x_{cm} = r^2\Delta\theta$

Correct Answer: C

The content provides the direct equation relating the translational displacement of the center of mass to the rotational displacement for a system rolling without slipping: $\Delta x_{cm}=r\Delta\theta$.