Q: A compact disk spins up from rest to an angular velocity of $$7200\ \text{rev/min} in$$ $$5.0\ \text{s}. $$What is its average angular acceleration in $$\text{rad/s}^2$$?

$$\alpha = 151\ \text{rad/s}^2$$

Q: A wheel rotates through an angular displacement of $$\Delta \theta = 2\pi$$ radians in $$4$$ seconds. What is its average angular velocity?

$$\omega_{\text{avg}} = \dfrac{\pi}{2}\ \text{rad/s}$$

Q: A point on the rim of a rotating wheel has a tangential acceleration $$a_{\text{tan}}$$ and a radial (centripetal) acceleration $$a_{\text{rad}}. $$Which of the following correctly expresses $$a_{\text{rad}}$$?

$$a_{\text{rad}} = r\$$omega^2$$

Q: If a rotating object has a constant angular acceleration $$\alpha$$, which equation gives the angular displacement $$\theta$$ after time $$t if it $$starts from rest?

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

Question 1

A compact disk spins up from rest to an angular velocity of $$7200\ 	ext{rev/min} in$$ $$5.0\ 	ext{s}. $$What is its average angular acceleration in $$	ext{rad/s}^2$$?

Accepted Answer

$$\alpha = 151\ 	ext{rad/s}^2$$

Question 2

Which of the following best describes the relationship between linear velocity $$v$$ and angular velocity $$\omega$$ for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = r\omega$$

Question 3

A wheel rotates through an angular displacement of $$\Delta 	heta = 2\pi$$ radians in $$4$$ seconds. What is its average angular velocity?

Accepted Answer

$$\omega_{	ext{avg}} = \dfrac{\pi}{2}\ 	ext{rad/s}$$

Question 4

If a merry-go-round rotates clockwise, which of the following statements about its angular velocity $$\omega is $$correct according to the sign convention?

Accepted Answer

$$\omega \u003c 0$$

Question 5

A bicycle wheel starts from rest and accelerates at $$2.0\ 	ext{rad/s}^2$$ for $$3.0\ 	ext{s}. $$What is its angular displacement during this time?

Accepted Answer

$$	heta = 6.0\ 	ext{rad}$$

Question 6

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

Accepted Answer

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

Question 7

A solid disk and a solid sphere of equal mass and radius are released from rest at the top of an incline. Which reaches the bottom first and why?

Accepted Answer

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

Question 8

A point on the rim of a rotating wheel has a tangential acceleration $$a_{	ext{tan}}$$ and a radial (centripetal) acceleration $$a_{	ext{rad}}. $$Which of the following correctly expresses $$a_{	ext{rad}}$$?

Accepted Answer

$$a_{	ext{rad}} = r\$$omega^2$$

Question 9

A force $$F is $$applied tangentially to a wheel of radius $$R. $$What is the resulting torque $$	au$$ about the center of the wheel?

Accepted Answer

$$	au = FR$$

Question 10

A uniform rod of length $$L$$ and mass $$M$$ rotates about an axis through one end perpendicular to its length. What is its moment of inertia?

Accepted Answer

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

Question 11

A rotating object slows down with a constant angular acceleration. If its initial angular velocity is $$\$$omega_0$$ and it comes to rest after time t$, what is the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = -\dfrac{\$$omega_0$$}{t}$$

Question 12

A child sits on a rotating merry-go-round at a distance $$r$$ from the center. If the angular velocity is doubled, what happens to the child's linear speed?

Accepted Answer

It is doubled.

Question 13

A disk of mass $$M$$ and radius $$R is $$rolling without slipping. What is the total kinetic energy of the disk?

Accepted Answer

$$K = \dfrac{3}{4} M v^2$

Question 14

A rotating airplane propeller increases its angular velocity from $$10\ 	ext{rad/s} to$$ $$30\ 	ext{rad/s} in$$ $$5\ 	ext{s}. $$What is its average angular acceleration?

Accepted Answer

$$\alpha = 4\ 	ext{rad/s}^2$$

Question 15

A solid cylinder and a hollow cylinder of equal mass and radius roll down an incline. Which reaches the bottom first and why?

Accepted Answer

The solid cylinder, because it has less rotational inertia.

Question 16

If a rotating object has a constant angular acceleration $$\alpha$$, which equation gives the angular displacement $$	heta$$ after time $$t if it $$starts from rest?

Accepted Answer

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

Rotational Motion: Concepts, Kinematics, and Energy

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