Question 1

A car's speedometer needle rotates about a fixed axis. If the needle moves through an angular displacement of $$	heta = 2.5$$ radians in 4.0 seconds, what is its average angular velocity?

Accepted Answer

$$0.625$$ rad/s

Question 2

Which of the following statements about the moment of inertia is correct?

Accepted Answer

It depends on both the mass distribution and the axis of rotation.

Question 3

A solid cylinder of mass $$M$$ and radius $$R$$ rotates about its central axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2}MR^2$

Question 4

An athlete whirls a discus in a circle of radius $$0.80 m at an $$angular speed of $$10.0$$ rad/s. What is the linear speed of the discus?

Accepted Answer

$$8.0 m/s$$

Question 5

A DVD starts from rest and accelerates at a constant angular acceleration $$\alpha = 5.0$$ rad/s$$^2. $$What is the angular displacement after $$0.40 s$$?

Accepted Answer

$$0.80$$ rad

Question 6

Which formula correctly relates the linear speed $$v of a $$point at a distance $$r$$ from the axis of rotation to the angular speed $$\omega$$?

Accepted Answer

$$v = r\omega$$

Question 7

A thin-walled hollow sphere of mass $$M$$ and radius $$R$$ rotates about its center. What is its moment of inertia?

Accepted Answer

$$I = MR^2$

Question 8

A turbine blade rotates with angular velocity $$\omega(t) = 2.00$$ rad/s $$- 2.10$$ rad/s$$^2 t. $$What is the angular acceleration at $$t = 9.10 s$$?

Accepted Answer

$$-19.1$$ rad/s$$^2$$

Question 9

A horizontal disk rotates about a vertical axis through its center. Point P is midway between the center and the rim, and point Q is on the rim. If the disk turns with constant angular velocity, which statement is true?

Accepted Answer

None of the above.

Question 10

If you double the radius of a rotating solid sphere while keeping its kinetic energy constant (mass unchanged), what must happen to its angular velocity?

Accepted Answer

It must be halved.

Question 11

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

Accepted Answer

$$K = \frac{1}{2}I\$$omega^2$$

Question 12

A bird flaps its wings rapidly because:

Accepted Answer

Its wings have a small moment of inertia.

Question 13

The parallel-axis theorem relates the moment of inertia $$I$$ about an axis a distance $$d$$ from the center of mass to the moment of inertia $$I_{cm}$$ about the center of mass. Which is the correct formula?

Accepted Answer

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

Question 14

A thin, very light wire is wrapped around a drum of mass $$m$$ and radius $$R$$ with moment of inertia $$I = \frac{1}{2}mR^2$. The free end is attached to a ball of mass m$. As the ball falls, the drum spins. At an instant when the ball has translational kinetic energy K$, what is the rotational kinetic energy of the drum?

Accepted Answer

$$K/2$$

Question 15

Which of the following is true for all points on a rigid body rotating about a fixed axis?

Accepted Answer

All points have the same angular acceleration.

Question 16

A solid sphere, a hollow sphere, and a solid cylinder all have the same mass and outer radius and the same rotational kinetic energy. Which object is rotating fastest?

Accepted Answer

The solid sphere.

Question 17

A block of mass $$m is $$attached to a cable wound around a solid cylinder of mass $$M$$ and radius $$R. $$The block is released from rest and falls a distance $$h. $$What is the speed $$v of $$the block as it hits the ground, assuming no friction and no slipping?

Accepted Answer

$$v = \sqrt{\frac{2mgh}{m + \frac{1}{2}M}}$$

Question 18

Why is it important to use radians rather than degrees when relating linear and angular quantities?

Accepted Answer

Radians are dimensionless and ensure correct proportionality in equations like $$s = r	heta.$$

Question 19

A slender rod of length $$L$$ and mass $$M$$ rotates about an axis through its center. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{12}ML^2$

Rotation of Rigid Bodies – Study Notes (University Physics, Chapter 9)

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