Q: A flywheel rotates such that it sweeps out an angle at the rate of $$\theta = \omega t = (45.0\,\text{rad/s})t. $$What is the angular velocity of the flywheel?

$$\omega = 45.0\,\text{rad/s}$$

Q: A bicycle mechanic mounts a bicycle and starts the rear wheel spinning from rest to a final angular velocity of $$250\,\text{rpm} in$$ $$5.00\,\text{s}. $$What is the average angular acceleration in $$\text{rad/s}^2$$?

$$\alpha = 5.24\,\text{rad/s}^2$$

Q: A flywheel is acted upon by three forces: $$F_1 = 20$$\,\text{N}$$, F_2$ = 30\,\text{N}$$, $$F_3 = 30$$\,\text{N}$$, all at a radius r = 0.5$$\,\text{m}$$. If F_1$ and F_2$ act in opposite directions and F_3$ acts perpendicular, what is the net torque?

$$\tau_{\text{net}} = 30\,\text{N}\cdot\text{m}$$

Q: A father pushes a $$500\,\text{kg}$$ merry-go-round of radius $$1.50\,\text{m}$$ with a force of $$250\,\text{N} at $$the edge. What is the angular acceleration produced, assuming the merry-go-round is a uniform disk?

$$\alpha = 1.13\,\text{rad/s}^2$$

Q: A $$120\,\text{N}\cdot\text{m}$$ torque is applied to a flywheel with moment of inertia $$300\,\text{kg}\cdot\text{m}^2$$ from rest. After eight revolutions, what is its angular velocity?

$$\omega = 2.53\,\text{rad/s}$$

Q: If a $$18.0\,\text{kg}$$ child sits $$1.25\,\text{m}$$ from the center of a $$500\,\text{kg}$$, $$1.50\,\text{m}$$ radius merry-go-round, how does the moment of inertia change?

It increases by $$18.0 \times (1.25)^2$

Question 1

Which equation correctly relates the moment of inertia $$I$$ for a system of particles to their masses and distances from the axis of rotation?

Accepted Answer

$$I = \sum_j m_j r_j^2$

Question 2

A solid sphere of mass $$M$$ and radius $$R$$ rotates about any diameter. What is its moment of inertia?

Accepted Answer

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

Question 3

A thin rod of mass $$M$$ and length $$l$$ rotates about an axis through its center perpendicular to its length. What is its moment of inertia?

Accepted Answer

$$I = \frac{Ml^2$}{12}$$

Question 4

A flywheel rotates such that it sweeps out an angle at the rate of $$	heta = \omega t = (45.0\,	ext{rad/s})t. $$What is the angular velocity of the flywheel?

Accepted Answer

$$\omega = 45.0\,	ext{rad/s}$$

Question 5

A bicycle mechanic mounts a bicycle and starts the rear wheel spinning from rest to a final angular velocity of $$250\,	ext{rpm} in$$ $$5.00\,	ext{s}. $$What is the average angular acceleration in $$	ext{rad/s}^2$$?

Accepted Answer

$$\alpha = 5.24\,	ext{rad/s}^2$$

Question 6

Which formula gives the rotational kinetic energy of a rotating object?

Accepted Answer

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

Question 7

A helicopter blade is modeled as a thin rod of mass $$500\,	ext{kg}$$ and length $$4.0\,	ext{m}$$ rotating about one end. What is its moment of inertia?

Accepted Answer

$$I = \frac{Ml^2$}{3}$$

Question 8

A hoop of mass $$M$$ and radius $$R$$ rotates about its cylinder axis. What is its moment of inertia?

Accepted Answer

$$I = MR^2$

Question 9

A flywheel is acted upon by three forces: $$F_1 = 20$$\,	ext{N}$$, F_2$ = 30\,	ext{N}$$, $$F_3 = 30$$\,	ext{N}$$, all at a radius r = 0.5$$\,	ext{m}$$. If F_1$ and F_2$ act in opposite directions and F_3$ acts perpendicular, what is the net torque?

Accepted Answer

$$	au_{	ext{net}} = 30\,	ext{N}\cdot	ext{m}$$

Question 10

A father pushes a $$500\,	ext{kg}$$ merry-go-round of radius $$1.50\,	ext{m}$$ with a force of $$250\,	ext{N} at $$the edge. What is the angular acceleration produced, assuming the merry-go-round is a uniform disk?

Accepted Answer

$$\alpha = 1.13\,	ext{rad/s}^2$$

Question 11

Which equation correctly relates torque $$	au to $$force $$F$$ and distance from the pivot $$r$$?

Accepted Answer

$$	au = r 	imes F$$

Question 12

A $$120\,	ext{N}\cdot	ext{m}$$ torque is applied to a flywheel with moment of inertia $$300\,	ext{kg}\cdot	ext{m}^2$$ from rest. After eight revolutions, what is its angular velocity?

Accepted Answer

$$\omega = 2.53\,	ext{rad/s}$$

Question 13

If a point on a flywheel is $$0.10\,	ext{m}$$ from the axis of rotation and the angular velocity is $$45.0\,	ext{rad/s}$$, what is the tangential speed?

Accepted Answer

$$v = 4.5\,	ext{m/s}$$

Question 14

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

Accepted Answer

Rotational kinetic energy is $$K = \frac{1}{2}I\$$omega^2$$ and translational kinetic energy is K$$ = \frac{1}{2}$$mv^2$$

Question 15

A thin rod of mass $$M$$ and length $$l$$ rotates about an axis through one end perpendicular to its length. What is its moment of inertia?

Accepted Answer

$$I = \frac{Ml^2$}{3}$$

Question 16

A merry-go-round is pushed with a force perpendicular to the radius. For maximum angular acceleration, where should the force be applied?

Accepted Answer

At the edge, perpendicular to the radius

Question 17

If a $$18.0\,	ext{kg}$$ child sits $$1.25\,	ext{m}$$ from the center of a $$500\,	ext{kg}$$, $$1.50\,	ext{m}$$ radius merry-go-round, how does the moment of inertia change?

Accepted Answer

It increases by $$18.0 	imes (1.25)^2$

Question 18

Which vector operation is used to calculate torque from force and position vectors?

Accepted Answer

Cross product

Chapter 10 Rotation and torque

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