Sections
Chapter Review

# Chapter Review

### Concept Items

#### 6.1Angle of Rotation and Angular Velocity

1.
One revolution is equal to how many radians? Degrees?
1. $1 rev = π rad = 180 ∘$
2. $1 rev = π rad = 360 ∘$
3. $1 rev = 2 π rad = 180 ∘$
4. $1 rev = 2 π rad = 360 ∘$
2.
What is tangential velocity?
1. Tangential velocity is the average linear velocity of an object in a circular motion.
2. Tangential velocity is the instantaneous linear velocity of an object undergoing rotational motion.
3. Tangential velocity is the average angular velocity of an object in a circular motion.
4. Tangential velocity is the instantaneous angular velocity of an object in a circular motion.
3.

What kind of motion is called spin?

1. Spin is rotational motion of an object about an axis parallel to the axis of the object.
2. Spin is translational motion of an object about an axis parallel to the axis of the object.
3. Spin is the rotational motion of an object about its center of mass.
4. Spin is translational motion of an object about its own axis.

#### 6.2Uniform Circular Motion

4.
What is the equation for centripetal acceleration in terms of angular velocity and the radius?
1. $a c = ω 2 r$
2. $a c = ω r$
3. $a c = r ω 2$
4. $a c = r ω$
5.
How can you express centripetal force in terms of centripetal acceleration?
1. $F c = a c 2 m$
2. $F c = a c m$
3. $F c = m a c 2$
4. $F c = m a c$
6.
What is meant by the word centripetal?
1. center-seeking
2. center-avoiding
3. central force
4. central acceleration

#### 6.3Rotational Motion

7.

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

1. the positive x direction of the coordinate system
2. the negative x direction of the coordinate system
3. the counterclockwise direction
4. the clockwise direction
8.
When you push a door closer to the hinges, why does it open more slowly?
1. It opens slowly, because the lever arm is shorter so the torque is large.
2. It opens slowly because the lever arm is longer so the torque is large.
3. It opens slowly, because the lever arm is shorter so the torque is less.
4. It opens slowly, because the lever arm is longer so the torque is less.
9.
When is angular acceleration negative?
1. Angular acceleration is the rate of change of the displacement and is negative when $ω$ increases.
2. Angular acceleration is the rate of change of the displacement and is negative when $ω$ decreases.
3. Angular acceleration is the rate of change of angular velocity and is negative when $ω$ increases.
4. Angular acceleration is the rate of change of angular velocity and is negative when $ω$ decreases.

### Critical Thinking Items

#### 6.1Angle of Rotation and Angular Velocity

10.
When the radius of the circular path of rotational motion increases, what happens to the arc length for a given angle of rotation?
1. The arc length is directly proportional to the radius of the circular path, and it increases with the radius.
2. The arc length is inversely proportional to the radius of the circular path, and it decreases with the radius.
3. The arc length is directly proportional to the radius of the circular path, and it decreases with the radius.
4. The arc length is inversely proportional to the radius of the circular path, and it increases with the radius.
11.
Consider a CD spinning clockwise. What is the sum of the instantaneous velocities of two points on both ends of its diameter?
1. $2 v$
2. $v 2$
3. $− v$
4. $0$

#### 6.2Uniform Circular Motion

12.
What are the directions of the velocity and acceleration of an object in uniform circular motion?
1. Velocity is tangential, and acceleration is radially outward.
2. Velocity is tangential, and acceleration is radially inward.
3. Velocity is radially outward, and acceleration is tangential.
4. Velocity is radially inward, and acceleration is tangential.
13.
Suppose you have an object tied to a rope and are rotating it over your head in uniform circular motion. If you increase the length of the rope, would you have to apply more or less force to maintain the same speed?
1. More force is required, because the force is inversely proportional to the radius of the circular orbit.
2. More force is required because the force is directly proportional to the radius of the circular orbit.
3. Less force is required because the force is inversely proportional to the radius of the circular orbit.
4. Less force is required because the force is directly proportional to the radius of the circular orbit.

#### 6.3Rotational Motion

14.

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

1. the top with the smaller radius because the radius of curvature is inversely proportional to the angular velocity
2. the top with the smaller radius because the radius of curvature is directly proportional to the angular velocity
3. the top with the larger radius because the radius of curvature is inversely proportional to the angular velocity
4. The top with the larger radius because the radius of curvature is directly proportional to the angular velocity
15.
A person tries to lift a stone by using a lever. If the lever arm is constant and the mass of the stone increases, what is true of the torque necessary to lift it?
1. It increases, because the torque is directly proportional to the mass of the body.
2. It increases because the torque is inversely proportional to the mass of the body.
3. It decreases because the torque is directly proportional to the mass of the body.
4. It decreases, because the torque is inversely proportional to the mass of the body.

### Problems

#### 6.1Angle of Rotation and Angular Velocity

16.
What is the angle of rotation (in degrees) between two hands of a clock, if the radius of the clock is $0.70 m$ and the arc length separating the two hands is $1.0 m$?
1. $40 ∘$
2. $80 ∘$
3. $81 ∘$
4. $163 ∘$
17.
A clock has radius of $0.5 m$. The outermost point on its minute hand travels along the edge. What is its tangential speed?
1. $9 × 10 − 4 m/s$
2. $3.4 × 10 − 3 m/s$
3. $8.5 × 10 − 4 m/s$
4. $1.3 × 10 1 m/s$

#### 6.2Uniform Circular Motion

18.

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

1. 192 N
2. 1, 111 N
3. 2, 300 N
4. 13, 333 N
19.

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.

1. 22 N
2. 667 N
3. 1, 500 N
4. 45, 000 N

#### 6.3Rotational Motion

20.

An object’s angular acceleration is 36 rad/s2. If it were initially spinning with a velocity of 6.0 m/s, what would its angular velocity be after 5.0 s?

21.

When a fan is switched on, it undergoes an angular acceleration of 150 rad/s2. How long will it take to achieve its maximum angular velocity of 50 rad/s?

1. −00.3 s
2. −0.3 s
3. 0.3 s
4. 3.0 s