AP Physics 1: Algebra-Based 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 11 questions to check your progress.
Question 1 of 11
All Questions (11)
A) $\sum F = 0$
B) $\sum \tau = 0$
C) $\omega = \text{constant}$
D) $\sum F = ma$
Correct Answer: B
According to the provided content, rotational equilibrium is the configuration where the net torque exerted on the system is zero. This is mathematically expressed as $\sum\tau = 0$. $\sum F = 0$ is the condition for translational equilibrium.
A) The net force exerted on the system is zero.
B) The system's moment of inertia is constant.
C) The net torque exerted on the system is zero.
D) The system is not in motion.
Correct Answer: C
The provided content explicitly states that 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.
A) There are no torques acting on the flywheel.
B) The net force on the flywheel is zero.
C) The flywheel is in translational equilibrium.
D) The net torque on the flywheel is zero.
Correct Answer: D
A constant angular velocity (like 3000 RPM) means the system is in rotational equilibrium. The condition for rotational equilibrium is that the net torque is zero ($\sum\tau = 0$). There could be balanced torques (e.g., from a motor and from friction), but their sum must be zero. We cannot conclude anything about the net force or translational equilibrium.
A) The net torque on the wrench is zero.
B) The net torque on the wrench is not balanced.
C) The wrench is in rotational equilibrium.
D) The net force on the wrench must be zero.
Correct Answer: B
The content states that if the torques on a system are not balanced (i.e., there is a net torque), the system's angular velocity must be changing. Since the wrench's angular velocity is decreasing, the torques are not balanced.
A) A book resting motionless on a desk.
B) A satellite in a stable circular orbit around the Earth.
C) A car's wheel spinning at a constant rate as the car accelerates forward.
D) A spinning top that is slowing down on the floor.
Correct Answer: C
The car's wheel spinning at a constant rate is in rotational equilibrium ($\sum\tau = 0$). However, because the car is accelerating, the wheel's center of mass is also accelerating, meaning it is not in translational equilibrium ($\sum F \neq 0$). This demonstrates that the two types of equilibrium are independent.
A) A system must be in translational equilibrium to be in rotational equilibrium.
B) A system in rotational equilibrium must also be in translational equilibrium.
C) A system can be in rotational equilibrium without being in translational equilibrium.
D) If the net force is zero, the net torque must also be zero.
Correct Answer: C
The provided content states that a system may exhibit rotational equilibrium without being in translational equilibrium, and vice versa. This means the two conditions are independent of each other.
A) Its center of mass accelerates, and its angular velocity remains constant.
B) Its center of mass moves at a constant velocity, and its angular velocity changes.
C) Its center of mass accelerates, and its angular velocity must be zero.
D) It is in both translational and rotational equilibrium.
Correct Answer: A
A non-zero net force causes a change in linear motion (acceleration of the center of mass), so it is not in translational equilibrium. A net torque of zero means the object is in rotational equilibrium, so its angular velocity remains constant (which could be zero or any other constant value).
A) The system's center of mass must accelerate.
B) The system's angular velocity must change.
C) The system must remain at rest.
D) The system will be in translational equilibrium.
Correct Answer: B
The content states that if the torques exerted on a rigid system are not balanced, the system’s angular velocity must be changing. This is the direct consequence of a non-zero net torque.
A) The sum of the torques must equal the moment of inertia.
B) The system must be stationary.
C) The net torque exerted on the system must be zero.
D) The net force exerted on the system must be zero.
Correct Answer: C
This is a direct restatement of the first condition provided in the content. A constant angular velocity is maintained if and only if the net torque on the system is zero.
A) The ball is in both rotational and translational equilibrium.
B) The ball is in rotational equilibrium, but not translational equilibrium.
C) The net torque on the ball is non-zero.
D) The net force on the ball is zero.
Correct Answer: C
The fact that the ball's angular velocity is increasing (from zero to some value) means it is not in rotational equilibrium. According to the corollary to Newton's second law, a changing angular velocity implies that the torques are not balanced, meaning the net torque is non-zero (caused by the friction force from the lane).
A) The merry-go-round is in rotational equilibrium because it is rotating.
B) The net torque on the merry-go-round is zero.
C) The angular velocity of the merry-go-round is constant.
D) The angular velocity of the merry-go-round is changing.
Correct Answer: D
The child's push creates a non-zero net torque, which causes the merry-go-round to spin faster. According to the provided content, if the torques are not balanced, the system's angular velocity must be changing. Therefore, the merry-go-round is not in rotational equilibrium.