PrepGo

AP Physics C: Mechanics Practice Quiz: Connecting Linear and Rotational Motion

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

A rigid circular disk is rotating about its center. Point P is located on the rim of the disk, and Point Q is located halfway between the center and the rim. Which of the following correctly compares the angular velocities of the two points?

All Questions (9)

A rigid circular disk is rotating about its center. Point P is located on the rim of the disk, and Point Q is located halfway between the center and the rim. Which of the following correctly compares the angular velocities of the two points?

A) The angular velocity of P is twice the angular velocity of Q.

B) The angular velocity of Q is twice the angular velocity of P.

C) The angular velocities of P and Q are equal.

D) The relationship cannot be determined without knowing the disk's rotation speed.

Correct Answer: C

For a rigid rotating system, all points within that system share the same angular displacement over the same time interval. Therefore, all points have the same angular velocity and angular acceleration, regardless of their distance from the axis of rotation.

A rigid circular disk is rotating about its center with a constant angular velocity. Point P is located on the rim of the disk at radius R, and Point Q is located halfway between the center and the rim at radius R/2. Which of the following correctly compares the linear velocities of the two points?

A) The linear velocity of P is equal to the linear velocity of Q.

B) The linear velocity of P is twice the linear velocity of Q.

C) The linear velocity of P is half the linear velocity of Q.

D) The linear velocity of P is four times the linear velocity of Q.

Correct Answer: B

The relationship between linear velocity and angular velocity is given by v = rω. Since the disk is a rigid system, both points have the same angular velocity (ω). Therefore, v_P = Rω and v_Q = (R/2)ω. This shows that v_P = 2v_Q.

A rigid turntable starts from rest and undergoes a constant angular acceleration. Point X is at a distance r from the center, and Point Y is at a distance 2r from the center. How does the tangential acceleration of Point Y (a_T,Y) compare to that of Point X (a_T,X)?

A) a_T,Y = 0.5 a_T,X

B) a_T,Y = a_T,X

C) a_T,Y = 2 a_T,X

D) a_T,Y = 4 a_T,X

Correct Answer: C

The tangential component of acceleration is given by the equation a_T = rα. Since the turntable is a rigid system, all points on it have the same angular acceleration (α). Therefore, the tangential acceleration is directly proportional to the radius. As Point Y is at twice the radius of Point X, its tangential acceleration is twice as large.

A point on the edge of a spinning wheel of radius r has a linear velocity v. If the wheel's angular velocity is doubled while the radius remains the same, what is the new linear velocity of the point?

A) v/2

B) v

C) 2v

D) 4v

Correct Answer: C

Linear velocity is related to angular velocity by the equation v = rω. Since the radius r is constant, the linear velocity v is directly proportional to the angular velocity ω. If ω is doubled, v must also double.

A small gear with radius r rotates with angular velocity ω, causing a point on its edge to have a linear velocity v. A larger gear with radius 3r rotates such that a point on its edge has the same linear velocity v. What is the angular velocity of the larger gear?

A) ω/9

B) ω/3

C) 3ω

D) 9ω

Correct Answer: B

For the small gear, the linear velocity is v = rω. For the large gear, the linear velocity is v = (3r)ω_large. Since the linear velocities are the same, we can set the expressions equal: rω = (3r)ω_large. Solving for the angular velocity of the large gear gives ω_large = rω / (3r) = ω/3.

The equation a_T = rα relates the angular acceleration (α) of a rotating rigid system to the linear acceleration of a point at radius r. What does the quantity a_T represent?

A) The centripetal acceleration, which points toward the center of rotation.

B) The total linear acceleration of the point.

C) The component of linear acceleration responsible for changing the point's speed.

D) The rate of change of the centripetal acceleration.

Correct Answer: C

a_T is the tangential component of acceleration. This component is tangent to the circular path of motion and is responsible for the change in the magnitude of the linear velocity (i.e., the speed). Centripetal acceleration is a separate component responsible for changing the direction of the velocity vector.

The angular velocity (ω) of a rigid rotating disk as a function of time is shown in a graph. At time t_1, the graph is a straight line with a positive slope. For a point on the rim of the disk at radius R, which statement is true about its motion at time t_1?

A) Its tangential acceleration is zero.

B) Its linear velocity is constant.

C) Its angular acceleration is positive and constant.

D) Its angular velocity is zero.

Correct Answer: C

Angular acceleration, α, is the rate of change of angular velocity, which corresponds to the slope of the ω vs. t graph. Since the slope is positive and constant at t_1, the angular acceleration α is positive and constant. This means the tangential acceleration (a_T = Rα) is also positive and non-zero, and the linear velocity is increasing, not constant.

A car's wheel is accelerating as the car speeds up. Why is it valid to use a single value for the angular acceleration, α, to describe the motion of the entire wheel, assuming it does not deform?

A) Because all points on the wheel have the same tangential acceleration.

B) Because the wheel is a rigid system, where all points rotate through the same angle in the same time interval.

C) Because the linear velocity is the same for all points on the wheel.

D) Because the angular acceleration is always constant for any rotating object.

Correct Answer: B

The definition of a rigid system is that all points on the object maintain their relative positions. This means all points rotate through the same angle in a given amount of time, which requires them to have the same angular velocity and the same angular acceleration. Tangential acceleration and linear velocity both depend on the radius and are not the same for all points.

Which of the following best describes the linear motion of a single point on the edge of a rotating rigid CD?

A) It has a constant linear velocity.

B) It has a linear velocity vector that is always tangent to its circular path.

C) It has a linear acceleration of zero.

D) It has the same linear motion as a point near the center of the CD.

Correct Answer: B

For any point in circular motion, its instantaneous linear velocity vector is always directed tangent to the circular path at that point. The velocity is not constant because its direction is continuously changing, which also means there is a non-zero (centripetal) acceleration. Its linear motion is different from a point near the center, which travels a smaller distance in the same time and thus has a smaller linear speed.