Question 1

A solid sphere and a hollow sphere have the same mass and radius. Which one has the larger moment of inertia about an axis through its center, and why?

Accepted Answer

The hollow sphere, because its mass is distributed farther from the axis.

Question 2

A wheel of radius $$R$$ rolls without slipping on a flat surface with angular speed $$\omega. $$What is the speed of the center of mass of the wheel?

Accepted Answer

$$v = R \omega$$

Question 3

A figure skater spins with her arms extended. When she pulls her arms in, which of the following quantities increases, assuming no external torque acts?

Accepted Answer

Her angular velocity

Question 4

A rod of length $$L$$ and mass $$M is $$pivoted at one end and released from rest at an angle $$	heta$$ above the horizontal. As the rod falls, what happens to its angular acceleration?

Accepted Answer

It increases as the rod falls.

Question 5

Which of the following best describes torque ($$	au$$)?

Accepted Answer

The product of force and the perpendicular distance from the axis of rotation.

Question 6

A hoop, a disk, and a solid sphere all have the same mass and radius and are released from rest at the top of an incline. Which one reaches the bottom first?

Accepted Answer

The solid sphere

Question 7

A particle of mass $$m$$ moves in a circle of radius $$r$$ with speed $$v. $$What is its angular momentum about the center of the circle?

Accepted Answer

$$L = mvr$$

Question 8

A student sits on a frictionless rotating stool holding a spinning bicycle wheel. If the student flips the wheel upside down, what happens to the angular momentum of the student plus stool system?

Accepted Answer

It remains the same in magnitude but reverses direction.

Question 9

If the net external torque on a system is zero, which of the following statements is true?

Accepted Answer

The system's angular momentum is conserved.

Question 10

A torque of $$10\ \mathrm{N \cdot m} is $$applied to a wheel with a moment of inertia $$2\ \mathrm{kg \cdot m^2$}. $$What is the angular acceleration of the wheel?

Accepted Answer

$$\alpha = 5\ \mathrm{$$rad/s^2$$}$$

Question 11

A rotating star contracts so that its radius decreases by a factor of 2. Assuming no external torque, what happens to its period of rotation?

Accepted Answer

It decreases by a factor of 1/4.

Question 12

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

Accepted Answer

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

Question 13

A wheel is rolling without slipping. What is the velocity of the point of the wheel in contact with the ground relative to the ground?

Accepted Answer

It is zero.

Question 14

A student is sitting at rest on a frictionless rotating stool and is handed a spinning wheel. If the student turns the wheel upside down, what will happen to the student?

Accepted Answer

The student will start rotating in the opposite direction to the wheel's original rotation.

Question 15

Which of the following best explains why a solid sphere reaches the bottom of an incline faster than a hoop of the same mass and radius?

Accepted Answer

The solid sphere has a smaller moment of inertia, so more of its potential energy is converted to translational kinetic energy.

Question 16

A torque is applied to a disk causing it to rotate from rest. Which of the following steps is NOT necessary when solving for the disk's angular acceleration?

Accepted Answer

Ignoring the axis of rotation.

Question 17

A rotating object has both translational and rotational kinetic energy. Which equation correctly expresses the total kinetic energy?

Accepted Answer

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

Question 18

Which of the following statements about angular momentum is correct?

Accepted Answer

Angular momentum is only conserved if the net external torque is zero.

Question 19

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

Accepted Answer

$$	au = Fr \sin 	heta$$

Question 20

A person sitting on a rotating stool with a spinning wheel in hand suddenly stops the wheel. What happens to the person?

Accepted Answer

The person starts spinning in the opposite direction to the wheel's original spin.

Rotational Motion, Dynamics, and Angular Momentum: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards