PrepGo

AP Physics 1: Algebra-Based Practice Quiz: Newton’s Second Law in Rotational Form

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

Test your understanding with short quizzes. This quiz has 10 questions to check your progress.

Question 1 of 10

Under which of the following conditions will the angular velocity of a system change?

All Questions (10)

Under which of the following conditions will the angular velocity of a system change?

A) When the net torque exerted on the system is zero.

B) When the net torque exerted on the system is not equal to zero.

C) When the rotational inertia of the system is very large.

D) When the system is analyzed using only linear methods.

Correct Answer: B

The provided content explicitly states, 'Angular velocity changes when the net torque exerted on the object or system is not equal to zero.'

According to Newton's Second Law in rotational form, what is the relationship between the net torque on a rigid system and its resulting angular acceleration?

A) They are inversely proportional and in opposite directions.

B) They are directly proportional and in the same direction.

C) They are independent of each other.

D) They are directly proportional but in opposite directions.

Correct Answer: B

The content specifies that 'The rate at which the angular velocity of a rigid system changes is directly proportional to the net torque exerted on the rigid system and is in the same direction.' The rate of change of angular velocity is the angular acceleration.

A constant non-zero net torque is applied to a rigid system. If the rotational inertia of the system is doubled, what happens to the angular acceleration?

A) It is quadrupled.

B) It is doubled.

C) It remains the same.

D) It is halved.

Correct Answer: D

Based on the formula $\sum\tau_{sys} = I_{sys}\alpha$, angular acceleration ($\alpha$) is inversely proportional to the rotational inertia ($I_{sys}$). If the rotational inertia is doubled while the net torque remains constant, the angular acceleration will be halved.

A rigid system is rotating with a constant, non-zero angular velocity. Which statement about the system must be true?

A) The net torque on the system must be zero.

B) The rotational inertia of the system must be zero.

C) A constant net torque is acting on the system.

D) The system cannot be described using linear analysis.

Correct Answer: A

The content states that 'Angular velocity changes when the net torque exerted on the object or system is not equal to zero.' If the angular velocity is constant, it is not changing. Therefore, the net torque exerted on the system must be zero.

Which equation correctly represents Newton's Second Law for a rotating rigid system?

A) $\sum\tau_{sys} = I_{sys} / \alpha$

B) $\sum\tau_{sys} = \alpha / I_{sys}$

C) $\sum\tau_{sys} = I_{sys}\alpha$

D) $\alpha = I_{sys}\sum\tau_{sys}$

Correct Answer: C

The provided text explicitly gives the formula for Newton's Second Law in rotational form as $\sum\tau_{sys} = I_{sys}\alpha$.

How is the angular acceleration of a rigid system related to its rotational inertia, assuming a constant net torque is applied?

A) It is directly proportional to the rotational inertia.

B) It is proportional to the square of the rotational inertia.

C) It is inversely proportional to the rotational inertia.

D) It is not related to the rotational inertia.

Correct Answer: C

The content states that 'The angular acceleration of the rigid system is inversely proportional to the rotational inertia of the rigid system.' This is also evident from the equation $\alpha = \sum\tau_{sys} / I_{sys}$.

Two disks, A and B, are subjected to the same non-zero net torque. Disk A has a larger rotational inertia than Disk B. Which of the following correctly compares their resulting angular accelerations?

A) Disk A will have a larger angular acceleration than Disk B.

B) Disk B will have a larger angular acceleration than Disk A.

C) Both disks will have the same angular acceleration.

D) The angular accelerations cannot be compared without knowing their angular velocities.

Correct Answer: B

According to the principle that angular acceleration is inversely proportional to rotational inertia ($\alpha = \sum\tau / I$), if both disks experience the same net torque, the disk with the smaller rotational inertia (Disk B) will have the larger angular acceleration.

To fully understand the motion of a rolling wheel, an analyst considers both the movement of its center of mass and its rotation about the center of mass. This approach is consistent with which statement from the provided content?

A) The net torque exerted on the object or system is not equal to zero.

B) The angular acceleration of the rigid system is inversely proportional to the rotational inertia.

C) To fully describe a rotating rigid system, linear and rotational analyses may need to be performed independently.

D) The rate at which the angular velocity of a rigid system changes is directly proportional to the net torque.

Correct Answer: C

This scenario directly illustrates the principle that 'To fully describe a rotating rigid system, linear and rotational analyses may need to be performed independently.' The movement of the center of mass is a linear analysis, while the rotation about it is a rotational analysis.

If a net torque is applied to a rigid body, causing it to experience an angular acceleration, what is the direction of the angular acceleration vector?

A) In the opposite direction of the net torque vector.

B) Perpendicular to the net torque vector.

C) In the same direction as the net torque vector.

D) In the direction of the angular velocity.

Correct Answer: C

The content states that the rate at which angular velocity changes (i.e., the angular acceleration) is 'in the same direction' as the net torque exerted on the rigid system.

If the net torque on a rigid system is doubled and its rotational inertia is halved, the resulting angular acceleration will be:

A) unchanged.

B) doubled.

C) halved.

D) quadrupled.

Correct Answer: D

From the equation $\alpha = \sum\tau_{sys} / I_{sys}$, angular acceleration is directly proportional to net torque and inversely proportional to rotational inertia. If torque is doubled ($\times 2$) and inertia is halved ($\times 1/2$), the new acceleration will be $(2) / (1/2) = 4$ times the original acceleration.