Q: A rigid body rotates with a constant angular acceleration. Which kinematic equation describes its angular displacement $$\theta$$ after time $$t$$?

$$\theta = \$$omega_0$$ t + \frac{1}{2}\alpha t^2$

Q: A satellite dish rotates from rest with a constant angular acceleration. If it completes $$\theta$$ radians in time $$t$$, what is the angular acceleration $$\alpha$$?

$$\alpha = \frac{2\theta}{t^2$}$$

Question 1

Which of the following statements best describes the moment of inertia (MOI) of a rigid body?

Accepted Answer

It depends on both the mass and how the mass is distributed relative to the axis of rotation.

Question 2

A solid cylinder and a ring, both with the same mass and radius, are released from rest at the top of an inclined ramp. Which will reach the bottom first and why?

Accepted Answer

The cylinder, because it has a smaller moment of inertia.

Question 3

Which equation correctly expresses the parallel axis theorem for the moment of inertia?

Accepted Answer

$$I = I_{cm} + MD^2$

Question 4

A meter stick of mass $$M$$ and length $$L is $$rotated about its end. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{3}ML^2$

Question 5

Which of the following best explains why it is more difficult to balance on a stopped bicycle than on a moving one?

Accepted Answer

A moving bicycle has greater angular velocity, which stabilizes it due to conservation of angular momentum.

Question 6

Which equation represents Newton’s second law for rotational motion?

Accepted Answer

$$	au_{net} = I\alpha$$

Question 7

A rigid body rotates with a constant angular acceleration. Which kinematic equation describes its angular displacement $$	heta$$ after time $$t$$?

Accepted Answer

$$	heta = \$$omega_0$$ t + \frac{1}{2}\alpha t^2$

Question 8

A figure skater pulls in her arms during a spin. What happens to her angular velocity and why?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases.

Question 9

Which of the following is the correct expression for the rotational kinetic energy of a rigid body?

Accepted Answer

$$K_{rot} = \frac{1}{2}I\$$omega^2$$

Question 10

A disk and a hoop, both with the same mass and radius, roll without slipping down an incline. Which reaches the bottom first and why?

Accepted Answer

The disk, because it has a smaller moment of inertia relative to its mass.

Question 11

Which of the following quantities is conserved in an isolated system with zero net external torque?

Accepted Answer

Rotational momentum (angular momentum)

Question 12

A satellite dish rotates from rest with a constant angular acceleration. If it completes $$	heta$$ radians in time $$t$$, what is the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{2	heta}{t^2$}$$

Question 13

Which of the following best describes the difference between mass and moment of inertia?

Accepted Answer

Mass is a measure of an object's resistance to linear acceleration, while moment of inertia is a measure of its resistance to rotational acceleration.

Question 14

A merry-go-round has children sitting at the edge and at the center. Which configuration makes it harder to start rotating the merry-go-round?

Accepted Answer

Children sitting at the edge, because the moment of inertia is larger.

Question 15

If the net torque on a rotating object is zero, what can be said about its angular momentum?

Accepted Answer

It remains constant.

Question 16

A rotating star collapses under gravity, reducing its radius to half its original value. If no external torque acts, what happens to its angular velocity?

Accepted Answer

It increases by a factor of 4.

Question 17

Which of the following is the correct relationship between torque $$	au$$, force $$F$$, and lever arm $$r$$?

Accepted Answer

$$	au = rF\sin	heta$$

Question 18

A rotating object has a constant angular velocity. What is the net torque acting on it?

Accepted Answer

Zero

Question 19

Which of the following is a real-world example of conservation of angular momentum?

Accepted Answer

A spinning ice skater pulling in her arms to spin faster.

Rotational Motion: Concepts, Equations, and Applications

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