Q: Which equation relates the angular displacement $$\theta to $$angular velocity $$\$$omega_0$$ and angular acceleration $$\alpha$$ for constant acceleration?

$$\theta = \$$theta_0$$ + \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Q: Which angular kinematic equation is analogous to $$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$ in linear motion?

$$\$$omega^2$$ = \$$omega_0$$^2 + 2 \alpha (\theta - \$$theta_0$$)$$

Question 1

Which of the following best describes the difference between a rigid body and a deformable body in rotational motion?

Accepted Answer

A rigid body maintains a fixed shape and size during rotation, while a deformable body can change its shape.

Question 2

A wheel starts from rest and accelerates at $$0.640$$ rad/s$$^2. $$How much time does it take to reach an angular velocity of $$140$$ rad/s?

Accepted Answer

Question 3

What is the formula for the moment of inertia $$I of a $$solid cylinder of mass $$M$$ and radius $$R$$ rotating about its central axis?

Accepted Answer

$$I = \frac{1}{2} M R^2$

Question 4

If a point on the edge of a record and a point near the center both complete one revolution in the same time, which statement is true?

Accepted Answer

The point on the edge has a greater linear speed than the point near the center.

Question 5

Which equation relates the angular displacement $$	heta to $$angular velocity $$\$$omega_0$$ and angular acceleration $$\alpha$$ for constant acceleration?

Accepted Answer

$$	heta = \$$theta_0$$ + \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Question 6

A yo-yo of mass $$0.10 kg $$and radius $$0.10 m $$descends a height $$0.40 m. $$What is its center-of-mass speed after descending, assuming no energy loss?

Accepted Answer

$$v = 2.29 m/s$$

Question 7

What is the relationship between the tangential velocity $$v_{tan}$$ and angular velocity $$\omega$$ for a point at distance $$r$$ from the axis?

Accepted Answer

$$v_{tan} = r \omega$$

Question 8

Which of the following best describes rolling without slipping?

Accepted Answer

$$v_{cm} = R \omega$$

Question 9

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

Accepted Answer

Solid sphere

Question 10

What is the kinetic energy of a rotating object with moment of inertia $$I$$ and angular velocity $$\omega$$?

Accepted Answer

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

Question 11

For a point particle of mass $$m at $$distance $$r$$ from the axis, what is its moment of inertia?

Accepted Answer

$$I = m r^2$

Question 12

Which equation gives the angular velocity $$\omega$$ after time $$t$$ for constant angular acceleration $$\alpha$$?

Accepted Answer

$$\omega = \$$omega_0$$ + \alpha t$$

Question 13

What is the radial acceleration $$a_{rad}$$ for a point moving in a circle of radius $$r$$ with tangential speed $$v$$?

Accepted Answer

$$a_{rad} = \frac{v^2$}{r}$$

Question 14

Which formula expresses the total kinetic energy of a rolling object?

Accepted Answer

$$K = \frac{1}{2} M v_{cm}^2 + \frac{1}{2} I_{cm} \$$omega^2$$

Question 15

A thin rectangular plate of mass $$M$$ and length $$L$$ rotates about its edge. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{3} M L^2$

Question 16

If a wheel rolls without slipping, what is the relationship between the distance $$s$$ traveled and the angle $$	heta$$ rotated?

Accepted Answer

$$s = R 	heta$$

Question 17

What is the gravitational potential energy of an extended-size object of mass $$M at $$height $$y_{cm}$$?

Accepted Answer

$$U_{grav} = M g y_{cm}$$

Question 18

Which angular kinematic equation is analogous to $$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$ in linear motion?

Accepted Answer

$$\$$omega^2$$ = \$$omega_0$$^2 + 2 \alpha (	heta - \$$theta_0$$)$$

Question 19

A hollow cylinder and a solid sphere of equal mass and radius roll down an incline. Why does the solid sphere reach the bottom first?

Accepted Answer

The solid sphere has a smaller moment of inertia, so more energy goes into translational motion.

Question 20

What is the angular acceleration $$\alpha if a $$wheel increases its angular velocity from $$0 to$$ $$140$$ rad/s in $$12.5 s$$?

Accepted Answer

Rotational Motion: Concepts, Equations, and Applications

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