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Test Prep

Multiple Choice

6.1 Angle of Rotation and Angular Velocity

What is 1 radian approximately in degrees?

57.3°
360°
π°
2π°

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

What are possible units for tangential velocity?

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

What is

30^{\circ}

in radians?

$\frac{π}{12}$
$\frac{π}{9}$
$\frac{π}{6}$
$\frac{π}{3}$

For a given object, what happens to the arc length as the angle of rotation increases?

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

What happens to centripetal acceleration as the radius of curvature decreases and the speed is constant, and why?

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.

10.

Why do we experience more sideways acceleration while driving around sharper curves?

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

11.

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

Rotation angle
Angular acceleration
Centripetal force
Angular velocity

12.

In the equation $τ = r F sin θ$ , what is F?

Linear force
Centripetal force
Angular force

13.

What happens when two torques act equally in opposite directions?

Angular velocity is zero.
Angular acceleration is zero.

14.

What is the mathematical relationship between angular and linear accelerations?

$a = r α$
$a = \frac{α}{r}$
$a = r^{2} α$
$a = \frac{α}{r^{2}}$

Short Answer

6.1 Angle of Rotation and Angular Velocity

15.

What is the rotational analog of linear velocity?

Angular displacement
Angular velocity
Angular acceleration
Angular momentum

16.

What is the rotational analog of distance?

Rotational angle
Torque
Angular velocity
Angular momentum

17.

What is the equation that relates the linear speed of a point on a rotating object with the object's angular quantities?

$v = \frac{ω}{r}$
$v = r ω$
$v = \frac{α}{r}$
$v = r α$

18.

As the angular velocity of an object increases, what happens to the linear velocity of a point on that object?

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.

19.

What is angular speed in terms of tangential speed and the radius?

$ω = \frac{v^{2}}{r}$
$ω = \frac{v}{r}$
$ω = r v$
$ω = r v^{2}$

20.

Why are radians dimensionless?

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

21.

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

22.

What are the standard units for centripetal acceleration?

m/s
${m/s}^{2}$
$m^{2} /s$
$m^{2} {/s}^{2}$

23.

What is the angle formed between the vectors of tangential velocity and centripetal force?

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

24.

What is the angle formed between the vectors of centripetal acceleration and centripetal force?

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

25.

What are the standard units for centripetal force?

m
m/s
m/s²
newtons

26.

As the mass of an object in uniform circular motion increases, what happens to the centripetal force required to keep it moving at the same speed?

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

27.

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.

28.

What is the kinematics relationship between

ω

α

, and

t

$ω = α t$
$ω = ω_{0} - α t$
$ω = ω_{0} + α t$
$ω = ω_{0} + \frac{1}{2} α t$

29.

What kind of quantity is torque?

Scalar
Vector
Dimensionless
Fundamental quantity

30.

If a linear force is applied to a lever arm farther away from the pivot point, what happens to the resultant torque?

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

31.

How can the same force applied to a lever produce different torques?

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

32.

Consider two pits on a CD, one close to the center and one close to the outer edge. When the CD makes one full rotation, which pit would have gone through a greater angle of rotation? Which one would have covered a greater arc length?

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.

33.

Consider two pits on a CD, one close to the center and one close to the outer edge. For a given angular velocity of the CD, which pit has a higher angular velocity? Which has a higher tangential velocity?

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.

34.

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

35.

Is an object in uniform circular motion accelerating? Why or why not?

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.

36.

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

37.

An object undergoes uniform circular motion. If the radius of curvature and mass of the object are constant, what is the centripetal force proportional to?

$F_{c} \propto \frac{1}{v}$
$F_{c} \propto \frac{1}{v^{2}}$
$F_{c} \propto v$
$F_{c} \propto v^{2}$

6.3 Rotational Motion

38.

Why do tornadoes produce more wind speed at the bottom of the funnel?

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.

39.

How can you maximize the torque applied to a given lever arm without applying more force?

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.

40.

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

Test Prep

Multiple Choice

6.1 Angle of Rotation and Angular Velocity

6.2 Uniform Circular Motion

6.3 Rotational Motion

Short Answer

6.1 Angle of Rotation and Angular Velocity

6.2 Uniform Circular Motion

6.3 Rotational Motion

Extended Response

6.1 Angle of Rotation and Angular Velocity

6.2 Uniform Circular Motion

6.3 Rotational Motion

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