Question 1

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 2

A child runs and jumps tangentially onto an initially stationary playground merry-go-round. As a result, the merry-go-round begins to turn. Explain in terms of the child-merry-go-round system.

Accepted Answer

The child has an initial angular momentum about the center of the merry-go-round. The total angular momentum of the system is conserved, so the merry-go-round must rotate when the child is on it.

Question 3

A stunt motorcyclist rides his motorcycle over a short ramp so that the motorcycle loses contact with the ground. As he does this, he guns his engine and the motorcycle's front wheel is observed to rise. Explain.

Accepted Answer

There is no external torque on the system, so the angular momentum is conserved. If the motorcycle is traveling from left to right, the increased clockwise angular momentum of the drive wheel requires a compensating counterclockwise angular momentum for the body of the motorcycle, thus raising the front end.

Question 4

The time rate of change of the total angular momentum of a system of particles equals the resultant external torque on the system.

Accepted Answer

This statement is a restatement of the principle of conservation of angular momentum, which states that the rate of change of angular momentum of a system is equal to the external torque acting on it.

Question 5

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 6

In general, precession results when
A)torque acts on a body with zero angular momentum.
B)the direction of torque acting on an object is parallel to the direction of angular momentum of the body.
C)there is no torque acting on a body.
D)the direction of torque acting on an object has a component perpendicular to the direction of angular momentum of the body.
E)the direction of torque acting on an object is opposite to the direction of angular momentum of the body.

Accepted Answer

Precession occurs when the torque applied to a rotating body has a component perpendicular to its angular momentum, causing the axis of rotation to change direction.

Question 7

If you cross a vector with itself, the resultant will be a unit vector.

Accepted Answer

The cross product of a vector with itself is always the zero vector, not a unit vector, because the sine of the angle between the vector and itself is zero.

Question 8

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

The answer of A merry-go-round spins freely when Janice moves...

Question 9

The total force on an object is zero. The angular momentum of the object
A)is zero.
B)may be changing.
C)can only be changing direction.
D)is constant.
E)can only be changing magnitude.

Accepted Answer

The answer of The total force on an object is...

Question 10

Vector cross products are not commutative.

Accepted Answer

The cross product of two vectors A and B is not commutative, meaning A × B is not equal to B × A; instead, A × B = -(B × A).

Question 11

For angular momentum to be conserved, the net force must be zero.

Accepted Answer

Angular momentum is conserved when the net external torque is zero, not the net force.

Question 12

For angular momentum to be conserved, the net torque must be zero.

Accepted Answer

Angular momentum is conserved when there is no external torque acting on a system, meaning the net torque is zero.

Question 13

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 when the net torque on a system is zero. If there is a net torque present, the angular momentum will change. Therefore, the correct answer is E, as the net torque not being zero is the only option that directly affects the conservation of angular momentum.

Question 14

A child is riding near the outer rim of a freely-rotating playground merry-go-round. What happens if the child walks towards the center?

Accepted Answer

The answer of A child is riding near the outer...

Question 15

Two nonparallel vectors determine a plane. Relative to the plane determined by the position vector where the force is applied and the force vector, in which direction is the torque vector about the origin?
A)perpendicular to the plane
B)in the plane, but perpendicular to both the position vector and the velocity vector
C)in the plane, but perpendicular to the velocity vector
D)in a direction dependent on the magnitudes of the velocity and position vectors
E)in the plane, but perpendicular to the position vector

Accepted Answer

The torque vector is given by the cross product of the position vector and the force vector, which results in a vector that is perpendicular to the plane formed by these two vectors.

Question 16

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 17

State the law of conservation of angular momentum for a rotating object.

Accepted Answer

The answer of State the law of conservation of angular...

Question 18

Two nonparallel vectors determine a plane. Relative to the plane determined by the position vector and velocity vector of a particle, in which direction is the angular momentum vector about the origin?
A)in the plane, but perpendicular to the velocity vector
B)in a direction dependent on the magnitudes of the velocity and position vectors
C)perpendicular to the plane
D)in the plane, but perpendicular to both the position vector and the velocity vector
E)in the plane, but perpendicular to the position vector

Accepted Answer

The angular momentum vector is perpendicular to the plane determined by the position and velocity vectors, as it is the cross product of these two vectors.

Question 19

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 kinetic energy: her moment of inertia is decreased, and so her angular speed must increase to conserve energy.
B)conservation of total energy: her moment of inertia is decreased, and so her angular speed must increase to conserve energy.
C)conservation of angular momentum: her moment of inertia is decreased, and so her angular speed must increase to conserve angular momentum.
D)Newton's second law for rotational motion: she exerts a torque and so her angular speed increases.
E)This has nothing to do with mechanics, it is simply a result of her natural ability to perform.

Accepted Answer

The skater's increase in angular speed is due to the conservation of angular momentum. When she pulls her arms in, her moment of inertia decreases, and to conserve angular momentum, her angular speed must increase.

Question 20

State the law of conservation of angular momentum for a system.

Accepted Answer

The answer of State the law of conservation of angular...

Quiz 11: Angular Momentum; General Rotation

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

A child runs and jumps tangentially onto an initially stationary playground merry-go-round. As a result, the merry-go-round begins to turn. Explain in terms of the child-merry-go-round system.

A stunt motorcyclist rides his motorcycle over a short ramp so that the motorcycle loses contact with the ground. As he does this, he guns his engine and the motorcycle's front wheel is observed to rise. Explain.

The time rate of change of the total angular momentum of a system of particles equals the resultant external torque on the system.

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

In general, precession results when

If you cross a vector with itself, the resultant will be a unit vector.

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

The total force on an object is zero. The angular momentum of the object

Vector cross products are not commutative.

For angular momentum to be conserved, the net force must be zero.

For angular momentum to be conserved, the net torque must be zero.

Angular momentum cannot be conserved if

A child is riding near the outer rim of a freely-rotating playground merry-go-round. What happens if the child walks towards the center?

Two nonparallel vectors determine a plane. Relative to the plane determined by the position vector where the force is applied and the force vector, in which direction is the torque vector about the origin?

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

State the law of conservation of angular momentum for a rotating object.

Two nonparallel vectors determine a plane. Relative to the plane determined by the position vector and velocity vector of a particle, in which direction is the angular momentum vector about the origin?

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

State the law of conservation of angular momentum for a system.