# Test Prep

### Multiple Choice

#### 6.1 Angle of Rotation and Angular Velocity

What is 1 radian approximately in degrees?

- 57.3°
- 360°
*π*°- 2
*π*°

If the following objects are spinning at the same angular velocities, the edge of which one would have the highest speed?

- Mini CD
- Regular CD
- Vinyl record

- $\text{m/s}$
- $\text{rad/s}$
- ${}^{\circ}\text{/s}$

- $\frac{\pi}{12}$
- $\frac{\pi}{9}$
- $\frac{\pi}{6}$
- $\frac{\pi}{3}$

- The arc length is directly proportional to the angle of rotation, so it increases with the angle of rotation.
- The arc length is inversely proportional to the angle of rotation, so it decreases with the angle of rotation.
- The arc length is directly proportional to the angle of rotation, so it decreases with the angle of rotation.
- The arc length is inversely proportional to the angle of rotation, so it increases with the angle of rotation.

#### 6.2 Uniform Circular Motion

Which of these quantities is constant in uniform circular motion?

- Speed
- Velocity
- Acceleration
- Displacement

Which of these quantities impact centripetal force?

- Mass and speed only
- Mass and radius only
- Speed and radius only
- Mass, speed, and radius all impact centripetal force

An increase in the magnitude of which of these quantities causes a reduction in centripetal force?

- Mass
- Radius of curvature
- Speed

- It increases, because the centripetal acceleration is inversely proportional to the radius of the curvature.
- It increases, because the centripetal acceleration is directly proportional to the radius of curvature.
- It decreases, because the centripetal acceleration is inversely proportional to the radius of the curvature.
- It decreases, because the centripetal acceleration is directly proportional to the radius of the curvature.

- Centripetal acceleration is inversely proportional to the radius of curvature, so it increases as the radius of curvature decreases.
- Centripetal acceleration is directly proportional to the radius of curvature, so it decreases as the radius of curvature decreases.
- Centripetal acceleration is directly proportional to the radius of curvature, so it decreases as the radius of curvature increases.
- Centripetal acceleration is directly proportional to the radius of curvature, so it increases as the radius of curvature increases.

#### 6.3 Rotational Motion

Which of these quantities is not described by the kinematics of rotational motion?

- Rotation angle
- Angular acceleration
- Centripetal force
- Angular velocity

In the equation $$\tau \text{=}rF\text{sin}\theta $$, what is *F*?

- Linear force
- Centripetal force
- Angular force

- Angular velocity is zero.
- Angular acceleration is zero.

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

### Short Answer

#### 6.1 Angle of Rotation and Angular Velocity

What is the rotational analog of linear velocity?

- Angular displacement
- Angular velocity
- Angular acceleration
- Angular momentum

What is the rotational analog of distance?

- Rotational angle
- Torque
- Angular velocity
- Angular momentum

- $v=\frac{\omega}{r}$
- $v=r\omega $
- $v=\frac{\alpha}{r}$
- $v=r\alpha $

- It increases, because linear velocity is directly proportional to angular velocity.
- It increases, because linear velocity is inversely proportional to angular velocity.
- It decreases because linear velocity is directly proportional to angular velocity.
- It decreases because linear velocity is inversely proportional to angular velocity.

- $\omega =\frac{{v}^{2}}{r}$
- $\omega =\frac{v}{r}$
- $\omega =rv$
- $\omega =r{v}^{2}$

- Radians are dimensionless, because they are defined as a ratio of distances. They are defined as the ratio of the arc length to the radius of the circle.
- Radians are dimensionless because they are defined as a ratio of distances. They are defined as the ratio of the area to the radius of the circle.
- Radians are dimensionless because they are defined as multiplication of distance. They are defined as the multiplication of the arc length to the radius of the circle.
- Radians are dimensionless because they are defined as multiplication of distance. They are defined as the multiplication of the area to the radius of the circle.

#### 6.2 Uniform Circular Motion

What type of quantity is centripetal acceleration?

- Scalar quantity; centripetal acceleration has magnitude only but no direction
- Scalar quantity; centripetal acceleration has magnitude as well as direction
- Vector quantity; centripetal acceleration has magnitude only but no direction
- Vector quantity; centripetal acceleration has magnitude as well as direction

- m/s
- ${\text{m/s}}^{2}\phantom{\rule{negativethinmathspace}{0ex}}$
- ${\text{m}}^{2}\text{/s}$
- ${\text{m}}^{2}\phantom{\rule{negativethinmathspace}{0ex}}{\text{/s}}^{2}\phantom{\rule{negativethinmathspace}{0ex}}$

- ${0}^{\circ}$
- ${30}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$
- ${90}^{\circ}$
- ${180}^{\circ}$

- ${0}^{\circ}$
- ${30}^{\circ}$
- ${90}^{\circ}$
- ${180}^{\circ}$

What are the standard units for centripetal force?

- m
- m/s
- m/s
^{2} - newtons

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

#### 6.3 Rotational Motion

The relationships between which variables are described by the kinematics of rotational motion?

- The kinematics of rotational motion describes the relationships between rotation angle, angular velocity, and angular acceleration.
- The kinematics of rotational motion describes the relationships between rotation angle, angular velocity, angular acceleration, and angular momentum.
- The kinematics of rotational motion describes the relationships between rotation angle, angular velocity, angular acceleration, and time.
- The kinematics of rotational motion describes the relationships between rotation angle, angular velocity, angular acceleration, torque, and time.

- $\omega =\alpha t$
- $\omega ={\omega}_{0}-\alpha t$
- $\omega ={\omega}_{0}+\alpha t$
- $\omega ={\omega}_{0}+\frac{1}{2}\alpha t$

What kind of quantity is torque?

- Scalar
- Vector
- Dimensionless
- Fundamental quantity

- It decreases.
- It increases.
- It remains the same.
- It changes the direction.

- By applying the force at different points of the lever arm along the length of the lever or by changing the angle between the lever arm and the applied force.
- By applying the force at the same point of the lever arm along the length of the lever or by changing the angle between the lever arm and the applied force.
- By applying the force at different points of the lever arm along the length of the lever or by maintaining the same angle between the lever arm and the applied force.
- By applying the force at the same point of the lever arm along the length of the lever or by maintaining the same angle between the lever arm and the applied force.

### Extended Response

#### 6.1 Angle of Rotation and Angular Velocity

- The one close to the center would go through the greater angle of rotation. The one near the outer edge would trace a greater arc length.
- The one close to the center would go through the greater angle of rotation. The one near the center would trace a greater arc length.
- Both would go through the same angle of rotation. The one near the outer edge would trace a greater arc length.
- Both would go through the same angle of rotation. The one near the center would trace a greater arc length.

- The point near the center would have the greater angular velocity and the point near the outer edge would have the higher linear velocity.
- The point near the edge would have the greater angular velocity and the point near the center would have the higher linear velocity.
- Both have the same angular velocity and the point near the outer edge would have the higher linear velocity.
- Both have the same angular velocity and the point near the center would have the higher linear velocity.

What happens to tangential velocity as the radius of an object increases provided the angular velocity remains the same?

- It increases because tangential velocity is directly proportional to the radius.
- It increases because tangential velocity is inversely proportional to the radius.
- It decreases because tangential velocity is directly proportional to the radius.
- It decreases because tangential velocity is inversely proportional to the radius.

#### 6.2 Uniform Circular Motion

- Yes, because the velocity is not constant.
- No, because the velocity is not constant.
- Yes, because the velocity is constant.
- No, because the velocity is not constant.

An object is in uniform circular motion. Suppose the centripetal force was removed. In which direction would the object now travel?

- In the direction of the centripetal force
- In the direction opposite to the direction of the centripetal force
- In the direction of the tangential velocity
- In the direction opposite to the direction of the tangential velocity

- ${F}_{c}\propto \frac{1}{v}$
- ${F}_{c}\propto \frac{1}{{v}^{2}\phantom{\rule{negativethinmathspace}{0ex}}}$
- ${F}_{c}\propto v$
- ${F}_{c}\propto {v}^{2}$

#### 6.3 Rotational Motion

- Wind speed is greater at the bottom because rate of rotation increases as the radius increases.
- Wind speed is greater at the bottom because rate of rotation increases as the radius decreases.
- Wind speed is greater at the bottom because rate of rotation decreases as the radius increases.
- Wind speed is greater at the bottom because rate of rotation decreases as the radius increases.

- The force should be applied perpendicularly to the lever arm as close as possible from the pivot point.
- The force should be applied perpendicularly to the lever arm as far as possible from the pivot point.
- The force should be applied parallel to the lever arm as far as possible from the pivot point.
- The force should be applied parallel to the lever arm as close as possible from the pivot point.

When will an object continue spinning at the same angular velocity?

- When net torque acting on it is zero
- When net torque acting on it is nonzero
- When angular acceleration is positive
- When angular acceleration is negative