Chapter 9

There are four ice skaters as shown in (Figure 1). Three skaters are spinning with equal rates of rotation, while the fourth skater is not spinning at all. Rank the skaters in terms of their angular momentum. Rank the skaters from largest to smallest angular momentum. To rank items as equivalent, overlap them.

3_2_1_4

What is meant by the "lever arm" of a torque?

It is the perpendicular distance from the rotational axis to the line along which the force acts.

On what does the angular momentum of an object depend? Select all that apply.

The shape of the object. The mass of the object. The rate at which that the object rotates. The axis of rotation.

When Dr. Hewitt cuts the broom right through the center of gravity, how do the weights of the two sides of the broom compare? View Available Hint(s)for Part B Hint 1for Part B. Center of gravity and weight distribution

The shorter side, where the bristles of the broom are, has a greater weight than the handle.

What kind of motion does a torque tend to impart to an object?

Torque tends to twist or change the state of rotation of the object.

Where is the center of gravity of the broom that Dr. Hewitt holds up? View Available Hint(s)for Part A Hint 1for Part A. Center of gravity and the balance point

at the balance point

What is the relationship between the center of gravity and support base for an object in stable equilibrium?

A vertical line through the center of gravity must pass inside the support base of the object.

Why doesn't the Leaning Tower of Pisa topple over?

A vertical line through the center of gravity passes inside its support base.

What is needed to change a system's angular momentum?

Angular momentum changes with an applied external torque.

How do linear momentum and angular momentum differ?

Angular momentum depends on the distribution of mass, whereas linear momentum depends on the total mass.

If a spinning skater pulls her arms in so as to reduce her rotational inertia by half, by how much will her rate of spin increase?

Angular momentum remains the same, while her rate of spin doubles.

Part complete Rank the torque needed to keep the stick steady, from largest to smallest. Rank from largest to smallest. To rank items as equivalent, overlap them.

B-C-A

Why it is easier to remove an old bolt if we add an extension to the wrench handle?

Because a higher torque is applied

Rank their chances for success from highest to lowest. (Note foot sizes) Rank the chances from highest to lowest. To rank items as equivalent, overlap them.

C_A_B

The experimenter from the video rotates on his stool, this time holding his empty hands in his lap. You stand on a desk above him and drop a long, heavy bean bag straight down so that it lands across his lap, in his hands. What happens? View Available Hint(s)for Part A Hint 1for Part A. How to approach the problem

He spins slower.

Under what condition is the angular momentum of an object conserved?

If there is no net torque acting on it.

If you toss a stick into the air, it appears to wobble all over the place. Specifically, about what place?

It will rotate about the center of mass.

Is your support base larger, smaller, or the same when you stand with your feet wide apart?

Larger.

How does the angular momentum of a cat change in falling from a tree?

The cat rotates its body through an angle, but the angular momentum of the cat remains constant.

Where is its center of mass for a baseball bat--closer to the grip or the thick end?

The center of mass is closer to the thick end.

For a rotating object experiencing no net external torque, what happens to the rate of rotation if the moment of inertia of the object decreases by a factor of 2?

The rate of rotation increases by a factor of 2.

How does the torque due to the weight of one side of the broom exerted around the balance point compare with the torque exerted by the weight of the other side of the broom around the balance point? View Available Hint(s)for Part C Hint 1for Part C. Net torque around balance point

The torque due to the weight of the shorter side (the bristles of the broom) is equal in magnitude to the torque due to the weight of the longer side, and opposite in direction.

How do clockwise and counterclockwise torques compare when a system is balanced?

They are equal in magnitude and opposite in direction.

A ruler is in equilibrium on the tip of your finger only if __________. View Available Hint(s)for Part A Hint 1for Part A. What are the conditions for equilibrium?

net torque and net force are zero

Part complete When a rock tied to a string is whirled in a horizontal circle, doubling the speed _______. View Available Hint(s)for Part A Hint 1for Part A. What equation about centripetal force can guide your thinking?

quadruples the tension in the string