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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