Q: A wheel of moment of inertia $$I is $$spinning with angular velocity $$\omega. If a $$torque $$\tau is $$applied for time $$t$$, what is the change in angular velocity?

$$\Delta \omega = \frac{\tau t}{I}$$

Question 1

A disk of mass $$M$$ and radius $$R is $$rotating about its central axis with angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

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

Question 2

Which equation correctly relates torque $$	au to $$force $$F$$ and lever arm $$r$$?

Accepted Answer

$$	au = F r \sin 	heta$$

Question 3

A uniform rod of length $$l$$ and mass $$m is $$pivoted at one end. What is its moment of inertia about the pivot?

Accepted Answer

$$I = \frac{1}{3} m l^2$

Question 4

If a force $$F is $$applied tangentially to the rim of a wheel of radius $$R$$, what is the resulting torque?

Accepted Answer

$$	au = F R$$

Question 5

Which of the following correctly expresses the parallel axis theorem for moment of inertia?

Accepted Answer

$$I_p = I_{cm} + M d^2$

Question 6

A block of mass $$m is $$attached to a rope wound around a pulley of mass $$M$$ and radius $$R. If $$the system is released from rest, what is the acceleration of the block, assuming the pulley rotates without friction?

Accepted Answer

$$a = \frac{m g}{m + \frac{1}{2} M}$$

Question 7

Which of the following is the correct relationship between linear and angular velocity for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = r \omega$$

Question 8

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

Accepted Answer

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

Question 9

Which formula gives the angular momentum $$L of a $$rigid body rotating about a fixed axis?

Accepted Answer

$$L = I \omega$$

Question 10

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping down an incline. What fraction of its total kinetic energy is rotational when it reaches the bottom?

Accepted Answer

$$\frac{2}{7}$$

Question 11

If a particle moves in a circle of radius $$r$$ with constant speed $$v$$, what is its angular velocity $$\omega$$?

Accepted Answer

$$\omega = \frac{v}{r}$$

Question 12

Which of the following is the correct expression for the arc length $$s$$ subtended by an angle $$	heta at $$radius $$r$$?

Accepted Answer

$$s = r 	heta$$

Question 13

A force $$F is $$applied at an angle $$	heta to a $$lever arm $$r. $$What is the magnitude of the torque produced?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 14

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

Accepted Answer

$$K_{rot} = \frac{1}{2} I \$$omega^2$$

Question 15

A wheel of moment of inertia $$I is $$spinning with angular velocity $$\omega. If a $$torque $$	au is $$applied for time $$t$$, what is the change in angular velocity?

Accepted Answer

$$\Delta \omega = \frac{	au t}{I}$$

Question 16

Which of the following is the correct expression for angular acceleration $$\alpha in $$terms of torque $$	au$$ and moment of inertia $$I$$?

Accepted Answer

$$\alpha = \frac{	au}{I}$$

Question 17

A rigid body rotates with angular velocity $$\omega$$ and has moment of inertia $$I. $$What is its angular momentum?

Accepted Answer

$$L = I \omega$$

Question 18

If a rotating object has a constant angular velocity, what is its angular acceleration?

Accepted Answer

$$\alpha = 0$$

Question 19

A disk of radius $$R$$ and mass $$M is $$spinning with angular velocity $$\omega. $$What is the total kinetic energy if it also moves linearly with velocity $$v$$?

Accepted Answer

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

Rotational Motion: Linear vs Angular Quantities, Kinematics, Torque, and Angular Momentum

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