Q: A disk rotates about a fixed axis with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$ and it rotates through an angular displacement $$\Delta \theta$$ in time t$, which equation correctly relates these quantities?

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

Q: Which of the following is true about the sign of torque $$\tau$$?

$$\tau \u003e 0$$ for forces that lead to counter-clockwise rotations about the pivot

Question 1

A disk rotates about a fixed axis with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$ and it rotates through an angular displacement $$\Delta 	heta$$ in time t$, which equation correctly relates these quantities?

Accepted Answer

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

Question 2

Which of the following best describes the moment of inertia $$I$$ for a system of $$N$$ point masses about a rotation axis?

Accepted Answer

$$I = \sum_{i=1}^N m_i r_i^2$

Question 3

A car moves in a circle of radius $$r at $$constant tangential speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

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

Question 4

A force $$F is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$\phi$$ with the lever arm. What is the magnitude of the torque produced?

Accepted Answer

$$	au = r F \sin \phi$$

Question 5

Which statement about angular acceleration $$\alpha is $$correct?

Accepted Answer

It is the rate of change of angular velocity: $$\alpha = \frac{d\omega}{dt}$$

Question 6

A hoop, disk, and sphere of equal mass $$M$$ and radius $$R$$ roll down an incline without slipping. Which has the smallest angular acceleration $$\alpha$$ for the same applied torque?

Accepted Answer

The hoop

Question 7

If a rigid body rotates with constant angular velocity $$\omega$$, what is the tangential speed $$v_t of a $$point at a distance $$r$$ from the axis?

Accepted Answer

$$v_t = r \omega$$

Question 8

A flywheel slows down with a constant angular acceleration $$\alpha$$ after the engine is shut off. If its initial angular velocity is $$\$$omega_0$$, how many revolutions N$ does it make before stopping?

Accepted Answer

$$N = \frac{\$$omega_0$$^2}{2 \alpha}$$

Question 9

Which of the following is the correct rotational analog of Newton's 2nd Law for a rigid body?

Accepted Answer

$$I \alpha = 	au_{net}$$

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

Question 11

A person swings a ball attached to a string in a horizontal circle at constant speed. What is the direction of the net force acting on the ball?

Accepted Answer

Toward the center of the circle

Question 12

Which of the following is true about the sign of torque $$	au$$?

Accepted Answer

$$	au \u003e 0$$ for forces that lead to counter-clockwise rotations about the pivot

Question 13

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

Accepted Answer

$$L = I \omega$$

Question 14

A disk and a hoop 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 disk, because it has a smaller moment of inertia

Question 15

If the net external torque on a system is zero, what can be said about its angular momentum?

Accepted Answer

Angular momentum is conserved

Question 16

A force $$F is $$applied tangentially to a solid sphere of mass $$M$$ and radius $$R at $$its surface. What is the resulting angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{F R}{\frac{2}{5} M R^2$}$$

Question 17

Which of the following is the correct expression for the total acceleration $$a of an $$object moving in a circle with tangential acceleration $$a_t$$ and centripetal acceleration $$a_c$$?

Accepted Answer

$$a = \sqrt{a_t^2$ + a_c^2$}$$

Question 18

A rod of length $$L is $$pivoted at one end and held horizontally. If a mass $$m is $$attached at the free end, what is the torque due to gravity about the pivot?

Accepted Answer

$$	au = m g L$$

Question 19

A rotating object has a moment of inertia $$I$$ and angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

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

Rotational Motion, Torque, and Angular Momentum: Study Notes

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