Q: A rotating plate is accelerated from rest to $$7.2\ \mathrm{rad/s} in$$ $$2.0\ \mathrm{s} by a $$constant torque. If its moment of inertia is $$1.5\ \mathrm{kg\cdot m^2$}$$, what is the torque?

$$\tau = I\alpha = 1.5 \times \dfrac{7.2}{2.0} = 5.4\ \mathrm{N\cdot m}$$

Q: A bucket of mass $$1.53\ \mathrm{kg}$$ hangs from a pulley of radius $$0.33\ \mathrm{m}$$ and moment of inertia $$0.385\ \mathrm{kg\cdot m^2$}. If $$the frictional torque is $$1.10\ \mathrm{N\cdot m}$$, what is the angular acceleration $$\alpha of $$the pulley?

$$\alpha = \dfrac{mg r - \tau_f}{I + mr^2$}$$

Q: A rotating object has an angular acceleration $$\alpha$$ and a moment of inertia $$I. If $$the net torque is doubled, what happens to the angular acceleration?

It doubles, since $$\alpha = \dfrac{\sum \tau}{I}.$$

Question 1

A bicycle wheel of radius $$0.34\ \mathrm{m}$$ slows down uniformly from $$8.40\ \mathrm{m/s} to $$rest over a distance of $$115\ \mathrm{m}. $$What is the initial angular velocity $$\$$omega_0$$ of the wheel?

Accepted Answer

$$\$$omega_0$$ = \dfrac{8.40}{0.34} = 24.7\ \mathrm{rad/s}$$

Question 2

Which of the following best describes the relationship between linear velocity $$v$$ and angular velocity $$\omega$$ for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = r\omega$$

Question 3

A solid sphere of mass $$m$$ and radius $$R$$ rolls without slipping down an incline from a height $$H. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{\dfrac{10}{7}gH}$$

Question 4

The moment of inertia of a uniform rod of mass $$m$$ and length $$L$$ about an axis through one end perpendicular to its length is:

Accepted Answer

$$I = \dfrac{1}{3}mL^2$

Question 5

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 $$	au$$ produced?

Accepted Answer

$$	au = rF\sin(	heta)$$

Question 6

A solid disk and a hoop, both with the same mass and radius, roll down an incline. Which reaches the bottom first and why?

Accepted Answer

The solid disk, because it has a smaller moment of inertia relative to its mass.

Question 7

The angular acceleration $$\alpha of a $$rotating object is related to the net torque $$\sum 	au$$ and the moment of inertia $$I by$$:

Accepted Answer

$$\sum 	au = I\alpha$$

Question 8

A point mass $$m is $$attached to a string and swung in a circle of radius $$r. $$What is its moment of inertia about the center?

Accepted Answer

$$I = mr^2$

Question 9

A rotating plate is accelerated from rest to $$7.2\ \mathrm{rad/s} in$$ $$2.0\ \mathrm{s} by a $$constant torque. If its moment of inertia is $$1.5\ \mathrm{kg\cdot m^2$}$$, what is the torque?

Accepted Answer

$$	au = I\alpha = 1.5 	imes \dfrac{7.2}{2.0} = 5.4\ \mathrm{N\cdot m}$$

Question 10

A bucket of mass $$1.53\ \mathrm{kg}$$ hangs from a pulley of radius $$0.33\ \mathrm{m}$$ and moment of inertia $$0.385\ \mathrm{kg\cdot m^2$}. If $$the frictional torque is $$1.10\ \mathrm{N\cdot m}$$, what is the angular acceleration $$\alpha of $$the pulley?

Accepted Answer

$$\alpha = \dfrac{mg r - 	au_f}{I + mr^2$}$$

Question 11

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

Accepted Answer

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

Question 12

A system consists of two masses, $$5.0\ \mathrm{kg}$$ and $$7.0\ \mathrm{kg}$$, mounted $$4.0\ \mathrm{m}$$ apart on a light rod. What is the moment of inertia about an axis halfway between the masses?

Accepted Answer

$$I = (5.0)(2.0)^2$ + (7.0)(2.0)^2$ = 48\ \mathrm{kg\cdot m^2$}$$

Question 13

The law of conservation of angular momentum states:

Accepted Answer

The total angular momentum of a system remains constant if the net external torque is zero.

Question 14

A solid cylinder (mass $$m$$, radius $$r) $$and a hollow sphere (same mass and radius) roll down an incline. Which has the greater acceleration and why?

Accepted Answer

The solid cylinder, because it has a smaller moment of inertia relative to its mass.

Question 15

If a rotating object has an angular velocity $$\omega$$ and a moment of inertia $$I$$, what is its angular momentum $$L$$?

Accepted Answer

$$L = I\omega$$

Question 16

A force of $$15.0\ \mathrm{N} is $$applied tangentially to a pulley of radius $$0.33\ \mathrm{m}$$, accelerating it from rest to $$30.0\ \mathrm{rad/s} in$$ $$3.00\ \mathrm{s}. If $$the frictional torque is $$1.10\ \mathrm{N\cdot m}$$, what is the moment of inertia $$I of $$the pulley?

Accepted Answer

$$I = \dfrac{(15.0)(0.33) - 1.10}{10.0} = 0.385\ \mathrm{kg\cdot m^2$}$$

Question 17

A rotating object has an angular acceleration $$\alpha$$ and a moment of inertia $$I. If $$the net torque is doubled, what happens to the angular acceleration?

Accepted Answer

It doubles, since $$\alpha = \dfrac{\sum 	au}{I}.$$

Question 18

A wheel rotates with a constant angular acceleration. Which equation correctly relates angular displacement $$	heta$$, initial angular velocity $$\$$omega_0$$, angular acceleration $$\alpha$$, and time t$?

Accepted Answer

$$	heta = \$$theta_0$$ + \$$omega_0$$ t + \dfrac{1}{2}\alpha t^2$

Rotational Kinematics and Dynamics: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards