# Chapter Review

### Concept Items

#### 6.1 Angle of Rotation and Angular Velocity

- $1\phantom{\rule{thinmathspace}{0ex}}\text{rev}=\pi \phantom{\rule{thinmathspace}{0ex}}\text{rad}={180}^{\circ}$
- $1\phantom{\rule{thinmathspace}{0ex}}\text{rev}=\pi \phantom{\rule{thinmathspace}{0ex}}\text{rad}={360}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$
- $1\phantom{\rule{thinmathspace}{0ex}}\text{rev}=2\pi \phantom{\rule{thinmathspace}{0ex}}\text{rad}={180}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$
- $1\phantom{\rule{thinmathspace}{0ex}}\text{rev}=2\pi \phantom{\rule{thinmathspace}{0ex}}\text{rad}={360}^{\circ}$

- Tangential velocity is the average linear velocity of an object in a circular motion.
- Tangential velocity is the instantaneous linear velocity of an object undergoing rotational motion.
- Tangential velocity is the average angular velocity of an object in a circular motion.
- Tangential velocity is the instantaneous angular velocity of an object in a circular motion.

What kind of motion is called *spin*?

- Spin is rotational motion of an object about an axis parallel to the axis of the object.
- Spin is translational motion of an object about an axis parallel to the axis of the object.
- Spin is the rotational motion of an object about its center of mass.
- Spin is translational motion of an object about its own axis.

#### 6.2 Uniform Circular Motion

- ${a}_{c}=\frac{{\omega}^{2}\phantom{\rule{negativethinmathspace}{0ex}}}{r}$
- ${a}_{c}=\frac{\omega}{r}$
- ${a}_{c}=r{\omega}^{2}\phantom{\rule{negativethinmathspace}{0ex}}$
- ${a}_{c}=r\omega \phantom{\rule{negativethinmathspace}{0ex}}$

- ${F}_{c}=\frac{{a}_{c}^{2}\phantom{\rule{negativethinmathspace}{0ex}}}{m}$
- ${F}_{c}=\frac{{a}_{c}}{m}$
- ${F}_{c}=m{a}_{c}^{2}\phantom{\rule{negativethinmathspace}{0ex}}$
- ${F}_{c}=m{a}_{c}$

- center-seeking
- center-avoiding
- central force
- central acceleration

#### 6.3 Rotational Motion

Conventionally, for which direction of rotation of an object is angular acceleration considered positive?

- the positive
*x*direction of the coordinate system - the negative
*x*direction of the coordinate system - the counterclockwise direction
- the clockwise direction

- It opens slowly, because the lever arm is shorter so the torque is large.
- It opens slowly because the lever arm is longer so the torque is large.
- It opens slowly, because the lever arm is shorter so the torque is less.
- It opens slowly, because the lever arm is longer so the torque is less.

- Angular acceleration is the rate of change of the displacement and is negative when $\omega $ increases.
- Angular acceleration is the rate of change of the displacement and is negative when $\omega $ decreases.
- Angular acceleration is the rate of change of angular velocity and is negative when $\omega $ increases.
- Angular acceleration is the rate of change of angular velocity and is negative when $\omega $ decreases.

### Critical Thinking Items

#### 6.1 Angle of Rotation and Angular Velocity

- The arc length is directly proportional to the radius of the circular path, and it increases with the radius.
- The arc length is inversely proportional to the radius of the circular path, and it decreases with the radius.
- The arc length is directly proportional to the radius of the circular path, and it decreases with the radius.
- The arc length is inversely proportional to the radius of the circular path, and it increases with the radius.

- $2v$
- $\frac{v}{2}$
- $-v$
- $0$

#### 6.2 Uniform Circular Motion

- Velocity is tangential, and acceleration is radially outward.
- Velocity is tangential, and acceleration is radially inward.
- Velocity is radially outward, and acceleration is tangential.
- Velocity is radially inward, and acceleration is tangential.

- More force is required, because the force is inversely proportional to the radius of the circular orbit.
- More force is required because the force is directly proportional to the radius of the circular orbit.
- Less force is required because the force is inversely proportional to the radius of the circular orbit.
- Less force is required because the force is directly proportional to the radius of the circular orbit.

#### 6.3 Rotational Motion

Consider two spinning tops with different radii. Both have the same linear instantaneous velocities at their edges. Which top has a higher angular velocity?

- the top with the smaller radius because the radius of curvature is inversely proportional to the angular velocity
- the top with the smaller radius because the radius of curvature is directly proportional to the angular velocity
- the top with the larger radius because the radius of curvature is inversely proportional to the angular velocity
- The top with the larger radius because the radius of curvature is directly proportional to the angular velocity

- It increases, because the torque is directly proportional to the mass of the body.
- It increases because the torque is inversely proportional to the mass of the body.
- It decreases because the torque is directly proportional to the mass of the body.
- It decreases, because the torque is inversely proportional to the mass of the body.

### Problems

#### 6.1 Angle of Rotation and Angular Velocity

- ${40}^{\circ}$
- ${80}^{\circ}$
- ${81}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$
- ${163}^{\circ}$

- $9\times {10}^{-4}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $3.4\times {10}^{-3}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $8.5\times {10}^{-4}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $1.3\times {10}^{1}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$

#### 6.2 Uniform Circular Motion

What is the centripetal force exerted on a 1,600 kg car that rounds a 100 m radius curve at 12 m/s?

- 192 N
- 1, 111 N
- 2, 300 N
- 13, 333 N

Find the frictional force between the tires and the road that allows a 1,000 kg car traveling at 30 m/s to round a 20 m radius curve.

- 22 N
- 667 N
- 1, 500 N
- 45, 000 N

#### 6.3 Rotational Motion

An object’s angular acceleration is 36 rad/s^{2}. If it were initially spinning with a velocity of 6.0 m/s, what would its angular velocity be after 5.0 s?

- 186 rad/s
- 190 rad/s
^{2} - −174 rad/s
- −174 rad/s
^{2}

When a fan is switched on, it undergoes an angular acceleration of 150 rad/s^{2}. How long will it take to achieve its maximum angular velocity of 50 rad/s?

- −00.3 s
- −0.3 s
- 0.3 s
- 3.0 s

### Performance Task

#### 6.3 Rotational Motion

Design a lever arm capable of lifting a 0.5 kg object such as a stone. The force for lifting should be provided by placing coins on the other end of the lever. How many coins would you need? What happens if you shorten or lengthen the lever arm? What does this say about torque?