Question 1

A car's speedometer needle rotates about a fixed axis. If the needle moves through an angle of $$	heta = 2.5$$ radians, and the radius from the axis to the tip of the needle is $$r = 0.12 m$$, what is the length of the arc traced by the tip of the needle?

Accepted Answer

$$s = 0.30 m$$

Question 2

Which of the following best describes the moment of inertia of a rigid body?

Accepted Answer

It is the sum of each particle's mass multiplied by the square of its distance from the axis of rotation: $$I = \sum m_i r_i^2$.

Question 3

A solid cylinder of mass $$M$$ and radius $$R$$ has a moment of inertia given by which formula?

Accepted Answer

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

Question 4

An athlete whirls a discus in a circle of radius $$r = 0.80 m. At a $$certain instant, the angular velocity is $$\omega = 10.0$$ rad/s and the angular acceleration is $$\alpha = 50.0$$ rad/s$$^2. $$What is the tangential acceleration of the discus?

Accepted Answer

$$a_t = 80.0 m/s$^2$$

Question 5

A DVD is initially at rest and begins to turn with a constant angular acceleration $$\alpha = 5.0$$ rad/s$$^2. $$After $$\Delta t = 0.40 s$$, what is the angle $$	heta$$ through which the DVD has rotated?

Accepted Answer

$$	heta = 0.80$$ rad

Question 6

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

Accepted Answer

All points have the same angular acceleration.

Question 7

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 8

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

Accepted Answer

It must be halved.

Question 9

The rotational kinetic energy of a rigid body rotating about an axis is given by:

Accepted Answer

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

Question 10

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

Accepted Answer

$$K$$

Question 11

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 12

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

$$\alpha = -19.1$$ rad/s$$^2$$

Question 13

Which of the following is the correct moment of inertia for a thin-walled hollow sphere of mass $$M$$ and radius $$R$$?

Accepted Answer

$$I = \frac{2}{3}MR^2$

Question 14

The parallel-axis theorem relates the moment of inertia $$I_p$$ about an axis parallel to and a distance $$d$$ from the center of mass axis. Which is the correct formula?

Accepted Answer

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

Question 15

A flywheel of diameter $$0.36 m $$has its angular position given by $$	heta = (2.0$$ rad/s$$) t. $$What is the angular velocity of the flywheel?

Accepted Answer

$$2.0$$ rad/s

Question 16

Which of the following is a correct statement about the use of radians in rotational motion equations?

Accepted Answer

Angles must always be expressed in radians when relating linear and angular quantities.

Question 17

A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?

Accepted Answer

$$0.616$$ rad/s$$^2$$

Question 18

Compared to a gear tooth on the rear sprocket (small radius) of a bicycle, a gear tooth on the front sprocket (large radius) has:

Accepted Answer

The same linear speed and a slower angular speed.

Rotation of Rigid Bodies – University Physics Chapter 9 Study Notes

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