Q: If a point on a rotating object has a tangential acceleration $$a_{\text{tan}}$$ and a centripetal acceleration $$a_c$$, what is the magnitude of the total linear acceleration $$a$$?

$$a = \sqrt{a_{\text{tan}}^2 + a_c^2$}$$

Q: If a rotating object has a constant angular acceleration $$\alpha$$, which equation gives its angular displacement $$\theta$$ after time $$t$$ from initial angular velocity $$\$$omega_0$$?

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

Q: If the angular velocity of a rotating object changes from $$\$$omega_0$$ to $$\omega$$ over an angular displacement $$\theta - \$$theta_0$$ with constant angular acceleration $$\alpha$$, which equation is correct?

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

Q: Which of the following is the correct vector equation for torque $$\vec{\tau}$$ produced by a force $$\vec{F} at $$position vector $$\vec{r}$$?

$$\vec{\tau} = \vec{r} \times \vec{F}$$

Question 1

Which of the following correctly expresses the relationship between angular displacement $$\Delta 	heta$$ and linear displacement $$s$$ for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$s = r \Delta 	heta$$

Question 2

A solid disk and a hollow ring, both with the same mass and radius, are spun with the same angular velocity $$\omega. $$Which has the greater rotational kinetic energy?

Accepted Answer

The hollow ring, because its moment of inertia is greater.

Question 3

Which equation gives the rotational kinetic energy $$K of a $$rigid body rotating about a fixed axis?

Accepted Answer

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

Question 4

A carousel accelerates uniformly from rest to an angular velocity $$\omega in $$time $$t. $$What is the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{\omega}{t}$$

Question 5

If a point on a rotating object has a tangential acceleration $$a_{	ext{tan}}$$ and a centripetal acceleration $$a_c$$, what is the magnitude of the total linear acceleration $$a$$?

Accepted Answer

$$a = \sqrt{a_{	ext{tan}}^2 + a_c^2$}$$

Question 6

Which of the following is the correct expression for the moment of inertia $$I of a $$system of particles?

Accepted Answer

$$I = \sum m_i r_i^2$

Question 7

A wheel rotates with constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$, what is its angular velocity $$\omega$$ after time t$?

Accepted Answer

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

Question 8

A cyclist is riding east. What is the direction of the angular velocity vector of the bicycle wheels?

Accepted Answer

Upward, perpendicular to the ground

Question 9

Which of the following correctly relates torque $$	au to $$angular acceleration $$\alpha$$ for a rigid body?

Accepted Answer

$$	au = I \alpha$$

Question 10

A rotating object has an angular velocity $$\omega$$ and radius $$r. $$What is the linear velocity $$v of a $$point on its edge?

Accepted Answer

$$v = \omega r$$

Question 11

If a rotating object has a constant angular acceleration $$\alpha$$, which equation gives its angular displacement $$	heta$$ after time $$t$$ from initial angular velocity $$\$$omega_0$$?

Accepted Answer

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

Question 12

A mass $$m is $$attached to the end of a massless rod of length $$r$$ and rotated about a fixed axis. What is the torque $$	au$$ produced by a tangential force $$F_t$$?

Accepted Answer

$$	au = r F_t$$

Question 13

Which of the following is the correct expression for the centripetal acceleration $$a_c of a $$point moving in a circle of radius $$r$$ with speed $$v$$?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 14

A rigid body rotates about a fixed axis with angular velocity $$\omega. $$Which statement is true about the linear velocities of its particles?

Accepted Answer

All particles have the same angular velocity, but different linear velocities depending on their distance from the axis.

Question 15

Which equation correctly relates the period $$T of $$uniform circular motion to the radius $$r$$ and speed $$v$$?

Accepted Answer

$$T = \frac{2 \pi r}{v}$$

Question 16

A rotating object has angular velocity $$\omega$$ and angular acceleration $$\alpha. $$What is the tangential acceleration $$a_{	ext{tan}} of a $$point at radius $$r$$?

Accepted Answer

$$a_{	ext{tan}} = \alpha r$$

Question 17

If the angular velocity of a rotating object changes from $$\$$omega_0$$ to $$\omega$$ over an angular displacement $$	heta - \$$theta_0$$ with constant angular acceleration $$\alpha$$, which equation is correct?

Accepted Answer

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

Question 18

A rotating object has angular velocity $$\omega$$ and radius $$r. $$What is its centripetal acceleration $$a_c$$?

Accepted Answer

$$a_c = \$$omega^2$$ r$$

Question 19

Which of the following is the correct vector equation for torque $$\vec{	au}$$ produced by a force $$\vec{F} at $$position vector $$\vec{r}$$?

Accepted Answer

$$\vec{	au} = \vec{r} 	imes \vec{F}$$

Rotational Motion: Definitions, Equations, and Physical Principles

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