AP Physics C: Mechanics 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 9 questions to check your progress.
Question 1 of 9
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A) When the system has a non-zero rotational inertia.
B) When a net external torque is applied to the system.
C) When a net external force is applied to the system's center of mass.
D) When the system is already rotating.
Correct Answer: B
According to the principles of rotational dynamics, a change in angular velocity (i.e., an angular acceleration) is caused by a non-zero net external torque. A net force causes linear acceleration, and an object can rotate at a constant angular velocity if the net torque is zero.
A) The angular acceleration is directly proportional to the rotational inertia.
B) The angular acceleration is inversely proportional to the rotational inertia.
C) The angular acceleration is equal to the rotational inertia.
D) There is no relationship between angular acceleration and rotational inertia.
Correct Answer: B
The relevant equation is $\sum\vec{\tau}_{net}=I_{sys}\vec{\alpha}$. Rearranging for angular acceleration gives $\vec{\alpha} = \sum\vec{\tau}_{net} / I_{sys}$. This shows that for a constant net torque, angular acceleration is inversely proportional to the rotational inertia.
A) Only a linear analysis of the forces causing the center of mass to accelerate.
B) Only a rotational analysis of the torques causing the cylinder to rotate.
C) Both independent linear and rotational analyses.
D) An analysis of the system's temperature change.
Correct Answer: C
The cylinder is both translating (its center of mass is moving down the ramp) and rotating. To fully describe this complex motion, both the linear motion (using F=ma) and the rotational motion (using τ=Iα) must be analyzed independently and then linked by the condition of rolling without slipping.
A) The system must be at rest.
B) The system's angular velocity must be constant.
C) The system's angular acceleration must be increasing.
D) The system's rotational inertia must be zero.
Correct Answer: B
From the equation $\sum\vec{\tau}_{net}=I_{sys}\vec{\alpha}$, if the net torque is zero, the angular acceleration ($\vec{\alpha}$) must also be zero. Zero angular acceleration means the angular velocity does not change; it remains constant. This constant value could be zero (at rest) or any other non-zero value.
A) Wheel A will have a greater angular acceleration than wheel B.
B) Wheel B will have a greater angular acceleration than wheel A.
C) Both wheels will have the same angular acceleration.
D) Both wheels will have the same angular velocity.
Correct Answer: A
Angular acceleration is given by $\alpha = \tau_{net} / I$. Since both wheels experience the same net torque, the wheel with the smaller rotational inertia (Wheel A) will have the greater angular acceleration. A larger rotational inertia indicates a greater resistance to changes in rotational motion.
A) The tendency of an object to continue rotating at a constant speed.
B) The amount of torque required to keep an object rotating.
C) The resistance of the system to a change in its angular velocity.
D) The total mass of the system multiplied by its angular velocity.
Correct Answer: C
Rotational inertia ($I_{sys}$) is the rotational analog of mass. It measures an object's resistance to changes in its state of rotational motion. A larger rotational inertia means a larger torque is required to produce the same angular acceleration.
A) $\alpha/2$
B) $\alpha$
C) $2\alpha$
D) $8\alpha$
Correct Answer: A
The original relationship is $\alpha = \tau / I$. The new angular acceleration, $\alpha'$, is given by the new torque divided by the new rotational inertia: $\alpha' = (2\tau) / (4I) = (2/4) * (\tau/I) = (1/2)\alpha$. The new angular acceleration is half of the original.
A) There is a net torque on the top, causing its angular velocity to change.
B) The rotational inertia of the top is decreasing.
C) The net torque on the top is zero, but its angular velocity is changing anyway.
D) A linear analysis is sufficient to describe the change in rotation.
Correct Answer: A
A change in angular velocity (in this case, a decrease) implies there is an angular acceleration. According to Newton's second law for rotation, an angular acceleration must be caused by a net external torque. The frictional forces create a torque that opposes the motion, causing the top to slow down.
A) Apply the force at half the distance from the bolt.
B) Apply the force at twice the distance from the bolt.
C) Use a wrench with half the rotational inertia.
D) It is impossible to achieve the same angular acceleration with less force.
Correct Answer: B
Torque is given by $\tau = rF_{\perp}$. To achieve the same torque (and thus the same angular acceleration, since $\tau = I\alpha$) with half the force ($F/2$), the lever arm ($r$) must be doubled. Applying the force at twice the distance from the bolt (the axis of rotation) will achieve this.