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AP Physics C: Mechanics Practice Quiz: Rotational Equilibrium and Newton's First 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 9 questions to check your progress.

Question 1 of 9

What is the defining condition for a system to be in rotational equilibrium?

All Questions (9)

What is the defining condition for a system to be in rotational equilibrium?

A) The net force exerted on the system is zero.

B) The net torque exerted on the system is zero.

C) The angular velocity of the system is zero.

D) The system is not accelerating linearly.

Correct Answer: B

The provided content explicitly defines rotational equilibrium as the configuration where the net torque exerted on the system is zero, represented by the equation $\sum\vec{\tau}_{i}=0$.

A spinning flywheel maintains a constant angular velocity. According to the rotational analog of Newton's first law, which of the following must be true?

A) There are no torques acting on the flywheel.

B) The net force on the flywheel is zero.

C) The flywheel has zero angular acceleration.

D) The net torque on the flywheel is zero.

Correct Answer: D

The rotational analog of Newton's first law states that a system will have a constant angular velocity if and only if the net torque exerted on the system is zero. Since the flywheel's angular velocity is constant, the net torque must be zero.

Which of the following scenarios describes a system that is NOT in rotational equilibrium?

A) A bicycle wheel spinning at a constant 30 revolutions per minute.

B) A door that is stationary and not rotating.

C) A spinning top that is gradually slowing down.

D) A planet rotating at a constant rate about its axis.

Correct Answer: C

Rotational equilibrium occurs when the net torque is zero, resulting in a constant angular velocity. A spinning top that is slowing down has a changing angular velocity, which means it has a non-zero angular acceleration. This requires a non-zero net torque, so it is not in rotational equilibrium.

The statement that a system's angular velocity remains constant only if the net torque is zero is known as:

A) The definition of rotational equilibrium.

B) The law of conservation of energy.

C) The rotational analog of Newton's first law.

D) The condition for translational equilibrium.

Correct Answer: C

The provided content directly identifies this principle: 'The rotational analog of Newton's first law is that a system will have a constant angular velocity only if the net torque exerted on the system is zero.'

If it is known that a rigid body is in rotational equilibrium, what can be definitively concluded about its motion?

A) The body must be stationary.

B) The body is moving with constant linear velocity.

C) The body's angular velocity is constant.

D) The net force on the body is zero.

Correct Answer: C

Rotational equilibrium means the net torque is zero. According to the rotational form of Newton's First Law, this implies the angular velocity is constant. This constant angular velocity could be zero (stationary) or a non-zero value (rotating at a constant rate). Therefore, the only definitive conclusion is that the angular velocity is constant.

Which equation mathematically expresses the condition for a system's angular velocity to remain constant?

A) $\sum\vec{F}_{i}=0$

B) $\sum\vec{\tau}_{i}=I\alpha$

C) $\sum\vec{p}_{i}=0$

D) $\sum\vec{\tau}_{i}=0$

Correct Answer: D

The content states that a constant angular velocity is maintained only if the net torque is zero. The mathematical representation for net torque being zero is $\sum\vec{\tau}_{i}=0$, which is the condition for rotational equilibrium.

Two opposing torques, $\vec{\tau}_A$ and $\vec{\tau}_B$, are applied to a disk. If the disk rotates at a constant speed, what is the relationship between the two torques?

A) Both torques must be zero.

B) $\vec{\tau}_A = \vec{\tau}_B$

C) $\vec{\tau}_A = -\vec{\tau}_B$

D) The magnitude of $\vec{\tau}_A$ must be greater than the magnitude of $\vec{\tau}_B$.

Correct Answer: C

For the disk to rotate at a constant speed (constant angular velocity), it must be in rotational equilibrium. This means the net torque must be zero: $\sum\vec{\tau}_{i} = \vec{\tau}_A + \vec{\tau}_B = 0$. This equation is satisfied only if one torque is the negative of the other, meaning they have equal magnitude and opposite direction.

The rotational analog of Newton's first law provides a direct relationship between which two physical quantities?

A) Net force and linear acceleration.

B) Net torque and angular velocity.

C) Mass and inertia.

D) Angular momentum and impulse.

Correct Answer: B

The law states that a constant angular velocity is maintained if and only if the net torque is zero. This establishes a direct conditional relationship between the net torque on a system and the state of its angular velocity (whether it is constant or changing).

A system is subject to multiple torques. If the system's angular velocity changes from +5 rad/s to -5 rad/s, which of the following statements must be true during that interval?

A) The system was in rotational equilibrium throughout the interval.

B) The net torque on the system was zero at all times.

C) The net torque on the system was non-zero for at least part of the interval.

D) The system's angular velocity was constant.

Correct Answer: C

According to the rotational analog of Newton's first law, angular velocity remains constant only when the net torque is zero. Since the angular velocity changed (from +5 rad/s to -5 rad/s), it was not constant. Therefore, the system was not in rotational equilibrium, and a non-zero net torque must have been exerted on it for at least part of the interval to cause this change.