Q: A wheel of radius $$0.5\ \mathrm{m}$$ and mass $$2\ \mathrm{kg} is $$rotating with an angular velocity of $$4\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

$$E = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} (0.25) \times 16 = 2\ \mathrm{J}$$

Q: A disk is subjected to a constant torque. Which of the following best describes its angular acceleration?

It is constant and given by $$\alpha = \frac{\tau}{I}.$$

Question 1

Which of the following best describes a rigid body in the context of rotational motion?

Accepted Answer

A body in which the distance between any two points remains constant during rotation.

Question 2

What is the correct formula for the moment of inertia $$I of a $$rigid body rotating about a fixed axis?

Accepted Answer

$$I = \sum m_i r_i^2$

Question 3

A solid disk of mass $$M$$ and radius $$R$$ rotates about its central axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2} M R^2$

Question 4

Which equation relates torque $$	au to $$angular acceleration $$\alpha$$ for a rigid body?

Accepted Answer

$$	au = I \alpha$$

Question 5

A wheel of radius $$0.5\ \mathrm{m}$$ and mass $$2\ \mathrm{kg} is $$rotating with an angular velocity of $$4\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$E = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} (0.25) 	imes 16 = 2\ \mathrm{J}$$

Question 6

If a rigid body rotates with constant angular velocity, which of the following statements is true?

Accepted Answer

The net external torque on the body is zero.

Question 7

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 8

Which of the following quantities is conserved when no external torque acts on a rigid body?

Accepted Answer

Angular momentum

Question 9

A figure skater pulls in her arms during a spin. What happens to her angular velocity and why?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases.

Question 10

A solid sphere and a hollow sphere of the same mass and radius are released from rest at the top of an incline. Which reaches the bottom first and why?

Accepted Answer

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

Question 11

Which of the following is the correct expression for the angular momentum $$L of a $$rigid body rotating with angular velocity $$\omega$$?

Accepted Answer

$$L = I \omega$$

Question 12

A disk is subjected to a constant torque. Which of the following best describes its angular acceleration?

Accepted Answer

It is constant and given by $$\alpha = \frac{	au}{I}.$$

Question 13

A rotating platform slows down due to friction. Which physical quantity is directly responsible for this change?

Accepted Answer

A nonzero external torque

Question 14

Which of the following is a correct analogy between linear and rotational motion?

Accepted Answer

Force is to mass as torque is to moment of inertia.

Question 15

A uniform disk of mass $$M$$ and radius $$R is $$spinning with angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$E = \frac{1}{2} I \$$omega^2$$ = \frac{1}{4} M R^2$ \$$omega^2$$

Question 16

A child sits on the edge of a freely rotating merry-go-round. If the child moves toward the center, what happens to the angular velocity of the system?

Accepted Answer

It increases because the moment of inertia decreases.

Rotation of Rigid Bodies: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard