Question 1

Which of the following statements about the center of mass (CM) of an object is correct?

Accepted Answer

The CM is the point where the object balances and acts as if all its mass were concentrated there.

Question 2

A car is moving at $$60\ \mathrm{mph}$$ ($$27.3\ \mathrm{m/s}) $$and its wheel radius is $$0.273\ \mathrm{m}. $$What is the angular velocity $$\omega of $$the wheel in $$\mathrm{rad/s}$$?

Accepted Answer

$$\omega = \dfrac{v}{r} = \dfrac{27.3}{0.273} = 39.9\ \mathrm{rad/s}$$

Question 3

Which equation correctly relates arc length $$s$$, radius $$r$$, and angle $$	heta in $$radians?

Accepted Answer

$$s = r 	heta$$

Question 4

A merry-go-round of mass $$500\ \mathrm{kg} is $$initially at rest. A $$60\ \mathrm{kg}$$ person walks clockwise on its edge at $$2\ \mathrm{m/s}. If $$the system is isolated, what happens to the merry-go-round?

Accepted Answer

It rotates counterclockwise to conserve angular momentum.

Question 5

Which formula gives the moment of inertia $$I$$ for a solid disk of mass $$m$$ and radius $$r$$ about its center?

Accepted Answer

$$I = \dfrac{1}{2} m r^2$

Question 6

If the axis of rotation of a disk is shifted a distance $$d$$ from its center, what is the new moment of inertia?

Accepted Answer

$$I = m r^2$ + m d^2$

Question 7

Which of the following best describes angular momentum conservation?

Accepted Answer

Angular momentum is conserved in the absence of external torques.

Question 8

A $$60\ \mathrm{kg}$$ person jumps onto the edge of a $$500\ \mathrm{kg}$$ merry-go-round spinning at $$10\ \mathrm{rpm}. $$What happens to the angular velocity of the system?

Accepted Answer

It decreases because the moment of inertia increases.

Question 9

Which equation correctly expresses rotational kinetic energy?

Accepted Answer

$$KE_{rot} = \dfrac{1}{2} I \$$omega^2$$

Question 10

A wheel has a mass $$m$$ and radius $$r. $$What is the total moment of inertia if the axis is shifted a distance $$d$$ from the center?

Accepted Answer

$$I = \dfrac{1}{2} m r^2$ + m d^2$

Question 11

If a person walks clockwise on the edge of a stationary merry-go-round, what is the direction of the merry-go-round's rotation?

Accepted Answer

Counterclockwise

Question 12

Which of the following is the correct unit for angular velocity $$\omega$$?

Accepted Answer

$$\mathrm{rad/s}$$

Question 13

A rotating object has an initial angular velocity $$\$$omega_0$$ and a final angular velocity $$\omega_f$$. What is the work done by torque during this change?

Accepted Answer

$$W = \dfrac{1}{2} I (\omega_f^2$ - \$$omega_0$$^2)$$

Question 14

Which of the following is true about the moment of inertia?

Accepted Answer

It depends on both the mass and how the mass is distributed relative to the axis of rotation.

Question 15

A person jumps onto a spinning merry-go-round, causing its angular velocity to decrease. Which principle explains this?

Accepted Answer

Conservation of angular momentum

Question 16

If the radius of the Earth is $$6.37 	imes 10^6$\ \mathrm{m}$$, what is the linear speed at the equator due to Earth's rotation?

Accepted Answer

$$v = \omega r = \dfrac{2\pi}{86400} 	imes 6.37 	imes 10^6$ = 463\ \mathrm{m/s}$$

Question 17

Which of the following best describes the difference between translational and rotational kinetic energy?

Accepted Answer

Translational kinetic energy depends on mass and velocity, while rotational kinetic energy depends on moment of inertia and angular velocity.

Question 18

A hollow sphere and a solid sphere of equal mass and radius roll down a ramp. Which reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia.

Question 19

Which of the following is the correct expression for angular acceleration $$\alpha in $$terms of change in angular velocity $$\omega$$ and time $$t$$?

Accepted Answer

$$\alpha = \dfrac{\Delta \omega}{\Delta t}$$

Physics Exam 3 Study Guide: Rotational Motion, Center of Mass, and Angular Momentum

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