Question 1

A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw?
A) It is impossible to say without knowing the masses.
B) It is impossible to say without knowing the distances.
C) The side the boy is sitting on will tilt downward.
D) Nothing, the seesaw will still be balanced.
E) The side the girl is sitting on will tilt downward.

Accepted Answer

When both move to half their original distance from the pivot, their torques decrease proportionally, maintaining balance.

Question 2

As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?
A) up
B) down
C) to your left
D) to your right
E) forwards

Accepted Answer

The answer of As you are leaving a building, the...

Question 3

You are walking holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. As you start to turn left, you feel the right side of the axle
A) push on your right hand toward the left.
B) push on your right hand toward you.
C) pull on your right hand away from you.
D) push on your right hand vertically up.
E) push on your right hand vertically down.

Accepted Answer

The answer of You are walking holding on to the...

Question 4

A person sits on a freely spinning lab stool (no friction). When this person extends her arms,
A) her moment of inertia decreases and her angular velocity increases.
B) her moment of inertia decreases and her angular velocity decreases.
C) her moment of inertia increases and her angular velocity increases.
D) her moment of inertia increases and her angular velocity decreases.
E) her moment of inertia increases and her angular velocity remains the same.

Accepted Answer

When the person extends her arms, her moment of inertia increases because the mass is farther away from the axis of rotation. However, her angular momentum must be conserved, so her angular velocity must decrease to compensate for the increase in moment of inertia. This can be seen in the equation L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity. If I increases, ω must decrease to maintain the same value of L.

Question 5

FIGURE 11-2 
-A croquet mallet balances when suspended from its center of mass, as shown in Figure 11-2. If you cut the mallet in two at its center of mass, as shown, how do the masses of the two pieces compare?
A) The masses are equal.
B) The piece with the head of the mallet has the greater mass.
C) The piece with the head of the mallet has the smaller mass.
D) It is impossible to tell.

Accepted Answer

The center of mass is closer to the heavier end, which is the head of the mallet, indicating that the piece with the head has a greater mass.

Question 6

An ice skater doing a spin pulls in her arms, decreasing her moment of inertia by a factor of two. How does her angular speed changes?
A) It is reduced by a factor of two.
B) It is reduced by a factor of four.
C) It increases by a factor of two.
D) It increases by a factor of four.
E) It doesn't change.

Accepted Answer

According to conservation of angular momentum, the product of moment of inertia and angular velocity is constant. When the ice skater reduces her moment of inertia by a factor of two, her angular velocity has to increase by a factor of two to keep the product constant. Therefore, her angular speed increases by a factor of two.

Question 7

A merry-go-round spins freely when Janice moves quickly to the center along a radius of the merry-go-round. It is true to say that
A) the moment of inertia of the system decreases and the angular speed increases.
B) the moment of inertia of the system decreases and the angular speed decreases.
C) the moment of inertia of the system decreases and the angular speed remains the same.
D) the moment of inertia of the system increases and the angular speed increases.
E) the moment of inertia of the system increases and the angular speed decreases.

Accepted Answer

When Janice moves to the center, the distribution of mass closer to the axis of rotation decreases the moment of inertia, and due to the conservation of angular momentum, the angular speed increases.

Question 8

When a car is weighed, it is allowed to move over a scale which records a reading as the front wheels go over the scale, and a second reading when the rear wheels go over the scale. The weight of the car is equal to
A) the weight under the front wheels.
B) the weight under the rear wheels.
C) the average of the two weights.
D) the sum of the two weights.
E) the difference of the two weights.

Accepted Answer

The weight of the car is the sum of the weight under the front wheels and the weight under the rear wheels. Therefore, option D is correct.

Question 9

You are holding a finishing sander with your right hand. The sander has a flywheel which spins counterclockwise as seen from behind the handle. You are sanding a wall in front of you. As you turn the sander towards the right, you feel a tendency in the sander to
A) turn towards the left.
B) turn upward.
C) turn downward.
D) push toward you.
E) pull away from you.

Accepted Answer

The answer of You are holding a finishing sander with...

Question 10

FIGURE 11-2 
-A puck moves on a horizontal air table. It is attached to a string that passes through a hole in the center of the table. As the puck rotates about the hole, the string is pulled downward very slowly and shortens the radius of rotation, so the puck gradually spirals in towards the center. By what factor will the puck's angular speed have changed when the string's length has decreased by 1/2?
A) 2
B) 4
C) 
D) 1
E) 1/2

Accepted Answer

The answer of FIGURE 11-2 
-A puck moves on a...

Question 11

FIGURE 11-1 
-The rotating systems shown in Figure 11-1 differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest,
A) the block at left lands first.
B) the block at right lands first.
C) both blocks land at the same time.
D) it is impossible to tell which block reaches the bottom first.

Accepted Answer

The block at right lands first because the masses are closer to the axis of rotation, reducing the moment of inertia and allowing the system to accelerate faster.

Question 12

FIGURE 11-1 -The rotating systems shown in Figure 11-1 differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom, respectively, then A) t_L = t_R. B) t_L = t_R. C) t_L = t_R. D) t_L = 2 t_R. E) t_L = 4t_R.

Accepted Answer

The answer of FIGURE 11-1 
-The rotating systems shown in...

Question 13

Two forces are applied to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second is
A) 1/4.
B) 1/2.
C) 2.
D) 4.
E) 8.

Accepted Answer

The torque (τ) of a force (F) applied at a distance (r) from the axis of rotation is given by τ = Fr. Since the forces are applied perpendicular to the door, the distance r is the same for both forces, and we can compare their torques simply by comparing the magnitudes of the forces. Let F1 be the larger force and F2 be the smaller force. Then we have F1 = 2F2, and the ratio of their torques is:

τ1/τ2 = (F1r)/(F2r) = (2F2r)/(F2r) = 2

So the answer is C, 2.

Question 14

FIGURE 11-2 
-A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her angular speed increases dramatically. The speed increase is a demonstration of
A) conservation of energy: her moment of inertia is decreased, and so her angular speed must increase to conserve energy.
B) conservation of angular momentum: her moment of inertia is decreased, and so her angular speed must increase to conserve angular momentum.
C) Newton's second law for rotational motion: she exerts a torque and so her angular speed increases.
D) This has nothing to do with mechanics, it is simply a result of her natural ability to perform.

Accepted Answer

The increase in angular speed is a demonstration of conservation of angular momentum. The skater's moment of inertia decreases as she brings her arms in, but her angular momentum must remain constant. Therefore, her angular speed increases to compensate for the decrease in moment of inertia and conserve angular momentum.

Question 15

FIGURE 11-2 
-A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her moment of inertia decreases by 1/2. By what factor does her rotational kinetic energy change?
A) 2
B) 4
C) 
D) 1/2
E) It doesn't change.

Accepted Answer

The answer of FIGURE 11-2 
-A figure skater is spinning...

Question 16

When you ride a bicycle, in what direction is the angular velocity of the wheels?
A) to your left
B) to your right
C) forwards
D) backwards
E) up

Accepted Answer

The answer of When you ride a bicycle, in what...

Question 17

FIGURE 11-3 
-A mill grinds corn by means of a grinding wheel attached to a long horizontal axle that is hinged to a vertical rotating axle as shown in Figure 11-3. The rotation of the vertical axle forces the horizontal axle to follow it. Thus, the wheel moves in a circular path, and its motion makes it rotate. The wheel then crushes the corn in its path. The force exerted by the wheel on the corn is
A) equal to the weight of the wheel.
B) greater than the weight of the wheel.
C) less than the weight of the wheel.
D) There is not enough information to answer this question.

Accepted Answer

The force exerted by the wheel on the corn is greater than the weight of the wheel, as the wheel is rotating and crushing the corn, thus applying a force greater than just its weight.

Question 18

FIGURE 11-2 
-A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her moment of inertia decreases by 1/2. Her angular speed increases by a factor of
A) 2.
B) 4.
C)  .
D) 1
E) 1/2.

Accepted Answer

The answer of FIGURE 11-2 
-A figure skater is spinning...

Question 19

FIGURE 11-2 
-Angular momentum cannot be conserved if
A) the angular acceleration changes.
B) the angular velocity changes.
C) there is a net force on the system.
D) the moment of inertia changes.
E) the net torque is not zero.

Accepted Answer

Angular momentum is conserved only when the net torque acting on the system is zero. If there is a non-zero net torque, then the angular momentum will change over time, regardless of whether the angular acceleration, angular velocity, or moment of inertia is changing. Therefore, choice E is the best choice.

Question 20

You are holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. In what direction do you need to apply a torque for the wheel to turn to the left?
A) toward you
B) away from you
C) vertically up
D) vertically down
E) to your right

Accepted Answer

To turn the wheel to the left, you need to apply a torque toward you, which will cause the wheel to precess to the left due to the gyroscopic effect.

Quiz 11: Rotational Dynamics and Static Equilibrium

A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw?

As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

You are walking holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. As you start to turn left, you feel the right side of the axle

A person sits on a freely spinning lab stool (no friction) . When this person extends her arms,

FIGURE 11-2 -A croquet mallet balances when suspended from its center of mass, as shown in Figure 11-2. If you cut the mallet in two at its center of mass, as shown, how do the masses of the two pieces compare?

An ice skater doing a spin pulls in her arms, decreasing her moment of inertia by a factor of two. How does her angular speed changes?

A merry-go-round spins freely when Janice moves quickly to the center along a radius of the merry-go-round. It is true to say that

When a car is weighed, it is allowed to move over a scale which records a reading as the front wheels go over the scale, and a second reading when the rear wheels go over the scale. The weight of the car is equal to

You are holding a finishing sander with your right hand. The sander has a flywheel which spins counterclockwise as seen from behind the handle. You are sanding a wall in front of you. As you turn the sander towards the right, you feel a tendency in the sander to

FIGURE 11-1 -The rotating systems shown in Figure 11-1 differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2 from the axis of rotation (right) . If you release the hanging blocks simultaneously from rest,

Two forces are applied to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second is

FIGURE 11-2 -A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her angular speed increases dramatically. The speed increase is a demonstration of

FIGURE 11-2 -A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her moment of inertia decreases by 1/2. By what factor does her rotational kinetic energy change?

When you ride a bicycle, in what direction is the angular velocity of the wheels?

FIGURE 11-2 -A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her moment of inertia decreases by 1/2. Her angular speed increases by a factor of

FIGURE 11-2 -Angular momentum cannot be conserved if

You are holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. In what direction do you need to apply a torque for the wheel to turn to the left?