Chapter 8

Assuming your feet are not held down, which is more difficult: doing sit-ups with your knees bent or with your legs straight out?

Legs straight out

Why are lightweight tires preferred in bicycle racing? Discuss and explain.

Less rotating mass.

Why is it easier to carry the same amount of water in two buckets, one in each hand, than in a single bucket?

The single bucket throws your center of gravity off balance.

Earth is not spherical but bulges at the equator. Jupiter bulges more. What is the cause of these bulges?

Because they spin.

When you pedal a bicycle, maximum torque is produced when the pedal sprocket arms are in the horizontal position, and no torque is produced when they are in the vertical position. Explain.

Force can make an object start moving, changes speeds, change direction, and stop moving.

Friction is needed for a car rounding a curve. But, if the road is banked, friction may not be required at all. What, then, supplies the needed centripetal force?

Gravity. Since the road is banked, the car would be attracted parallel to the banked road, toward the center of the radius of curvature.

While riding on a carnival Ferris wheel, Sam Nasty horses around and climbs out of his chair and along the spoke so that he is halfway to the axis.How does his rotational speed compare with that of his friends who remain in the chair? How does his tangential speed compare? Why are your answers different?

His rotational speed doesn't change because he is still a part of a moving body, but his tangential speed is less than those of his friends.

A racing car on a flat circular track needs friction between the tires and the track to maintain its circular motion. How much more friction is required for twice the speed?

If speed is increased by twice the original speed, the friction will need to be four times as much.

If all of Earth's inhabitants moved to the equator, how would this affect Earth's rotational inertia? How would it affect the length of a day?

Increase rotational inertia, by angular momentum conservation, the rotation of the earth would decrease making days longer

When a car drives off a cliff it rotates forward as it falls. For a higher speed off the cliff, discuss whether the car will rotate more or less.

It will rotate with a greater angular velocity when it is travelling slowly.

Is the net torque changed when a partner on a seesaw stands or hangs from her end instead of sitting? (Does the weight or the lever arm change?)

No because the distance that the force is applied on is still the same.

If the world's populations moved to the North Pole and the South Pole, would the 24-hour day become longer, shorter, or stay the same?

Shorter

Which will have the greater acceleration rolling down an incline: a bowling ball or a volleyball? Defend your answer.

The bowling ball because it has less rotational inertia per unit mass.

Using the ideas of torque and center of gravity, explain why a ball rolls down a hill.

The center of gravity of the ball is perpendicular to the earth. If it is on a level surface, the center of gravity coincides with where the ball touched the surface. Thus, there is no lever arm and 0 torque to start rolling

A large wheel is coupled to a wheel with half the diameter. How does the rotational speed of the smaller wheel compare with that of the larger wheel?

The tangential speeds are equal - same speed as the belt. The smaller wheel rotates twice as fast because for the same tangential speed, and r half, w must be twice. v(big wheel) = rw(small wheel) = (r/2 x 2w)

Why must you bend forward when carrying a heavy load on your back?

To distribute your mass so the center of gravity is above your support base.

When a bowling ball leaves your hand, it may not spin. But farther along the alley, it does spin. What produces the spinning?

Torque

Explain why a centripetal force does not do work on a circularly moving object.

When you move in a circle, centripetal force is always directed toward the inside of the circle, which is exactly perpendicular to your direction of motion in the circle. Since the force is perpendicular to the direction of motion, there is no work done.

Why does a typical small helicopter with a single main rotor have a second small rotor on its tail? Describe the consequence if the small rotor fails in flight.

Without the small rotor on its tail, the helicopter and the main rotor would rotate in opposite directions. The small rotor provides a torque to offset the rotational motion that the helicopter would otherwise have.

As a car speeds up when rounding a curve, does the centripetal force on the car also increase? Defend your answer.

Yes - increased speed at the same radical distance means greater centripetal force. If greater centripetal force isn't applied, the car will skid.

Flamingos are frequently seen standing on one leg with the other leg lifted. Is rotational inertia enhanced with long legs? What can you say about the bird's center of mass with respect to the foot on which it stands?

Yes, rotational inertia is enhanced with long legs. The bird's foot is directly below the bird's center of mass