Q: A disk starts from rest and undergoes a constant angular acceleration $$\alpha. $$What is its angular displacement $$\Delta \theta$$ after time $$t$$?

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

Q: A rotating object has a net torque $$\tau_{net}$$ and moment of inertia $$I. $$What is its angular acceleration $$\alpha$$?

$$\alpha = \frac{\tau_{net}}{I}$$

Question 1

A car of mass $$m$$ moves in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of the centripetal acceleration acting on the car?

Accepted Answer

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

Question 2

Which of the following correctly relates angular velocity $$\omega$$ and tangential speed $$v_t$$ for an object moving in a circle of radius $$r$$?

Accepted Answer

$$v_t = \omega r$$

Question 3

A disk starts from rest and undergoes a constant angular acceleration $$\alpha. $$What is its angular displacement $$\Delta 	heta$$ after time $$t$$?

Accepted Answer

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

Question 4

A force $$F is $$applied perpendicular to a lever arm of length $$r. $$What is the torque $$	au$$ produced about the pivot?

Accepted Answer

$$	au = rF$$

Question 5

Which statement about the center of gravity of a uniform object is correct?

Accepted Answer

It is located at the geometric center of the object.

Question 6

A solid sphere of mass $$M$$ and radius $$R$$ rotates about an axis through its center. What is its moment of inertia $$I$$?

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 7

A rotating object has a net torque $$	au_{net}$$ and moment of inertia $$I. $$What is its angular acceleration $$\alpha$$?

Accepted Answer

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

Question 8

A figure skater pulls in her arms while spinning, reducing her moment of inertia. What happens to her angular velocity, assuming no external torque?

Accepted Answer

Her angular velocity increases.

Question 9

A ball of mass $$m is $$dropped from height $$h. $$What is its kinetic energy just before hitting the ground, neglecting air resistance?

Accepted Answer

$$K = mgh$$

Question 10

A block slides down a frictionless incline. Which principle allows you to equate its initial potential energy to its final kinetic energy?

Accepted Answer

Conservation of energy

Question 11

A force $$F$$ acts on a mass $$m$$ for a time $$\Delta t. $$What is the impulse delivered to the mass?

Accepted Answer

$$J = F \Delta t$$

Question 12

A 2 kg object moving at 3 m/s collides with a stationary 1 kg object. If they stick together, what is their final velocity?

Accepted Answer

$$v_f = 2 m/s$$

Question 13

Which equation expresses the work-energy theorem?

Accepted Answer

$$W = \Delta K$$

Question 14

A rotating wheel has an initial angular velocity $$\omega_i$$ and angular acceleration $$\alpha. $$What is its angular velocity $$\omega_f$$ after time $$t$$?

Accepted Answer

$$\omega_f = \omega_i + \alpha t$$

Question 15

A seesaw is balanced when two children sit at different distances from the pivot. What physical quantity must be equal for both sides to balance?

Accepted Answer

The torques about the pivot

Question 16

A ball is thrown upward with velocity $$v_0. At $$its highest point, what is its kinetic energy?

Accepted Answer

$$K = 0$$

Question 17

Which of the following is true about momentum in a closed system with no external forces?

Accepted Answer

Total momentum is conserved.

Question 18

A rotating rod of length $$L$$ and mass $$M$$ rotates about its end. What is its moment of inertia?

Accepted Answer

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

Question 19

A child pushes a merry-go-round, causing it to accelerate. Which equation relates the net torque and angular acceleration?

Accepted Answer

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

Exam 2 Review: Rotational Motion, Torque, Momentum, and Energy in Physics

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