Chapter 8

The rock and meterstick balance at the 25-cm mark, as shown. The meterstick has a mass of 0.60 kg . What must be the mass of the rock?

.6 kg

Calculate the torque produced by a 60-N perpendicular force at the end of a 0.22-m-long wrench.

13 N m

Calculate the torque produced by a 60-N force when a pipe extends the length of the wrench to 0.46 m

28 N m

Calculate the angular momentum of the person if the force of friction that keeps a 95-kg person sitting on the edge of a horizontal rotating platform when the person sits 1.8 m from the center of the platform and has a tangential speed of 3.2 m/s .

550 kg x m^2 /s

Calculate the angular momentum of the person if the force of friction that keeps a 95-kg person sitting on the edge of a horizontal rotating platform when the person sits 1.9 m from the center of the platform and has a tangential speed of 3.4 m/s .

610 kg x m^2 /s

the force of friction that keeps a 55-kg person sitting on the edge of a horizontal rotating platform when the person sits 1.9 m from the center of the platform and has a tangential speed of 6.4 m/s , what will be the person's angular momentum?

670 kg x m^2 /s

Calculate the tension in a horizontal string that whirls a 1.5-kg toy in a circle of radius 2.1 m when it moves at 3.2 m/s on an icy surface.

7.3 N

Calculate the tension in a horizontal string that whirls a 2.1-kg toy in a circle of radius 2.9 m when it moves at 3.3 m/s on an icy surface.7.9 N

7.9 N

Calculate the tension in a horizontal string that whirls a 2.0-kg toy in a circle of radius 2.0 m when it moves at 2.9 m/s on an icy surface.

8.4 N

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

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

Why can't you stand with your heels and back to a wall and then bend over to touch your toes and return to your stand-up position?

A vertical line through the center of gravity of your body is in front of the tips of your toes, which is outside your support base.

Why doesn't the leaning tower of Pisa topple over?

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

Distinguish between linear momentum and angular momentum.

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

What is the law of inertia for rotating systems in terms of angular momentum?

Angular momentum does not change without an applied external torque.

If a skater who is spinning pulls her arms in so as to reduce her rotational inertia by half, by how much will her angular momentum change? By how much will her rate of spin change?

Her angular momentum does not change. Her rotational speed doubles.

Why is centrifugal force in a rotating frame called "fictitious force"?

It is not a fundamental force of nature. Instead, it is a force that only appears in an accelerating frame of reference.

What is it 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.

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

It will rotate at about the center of mass.

If the string that holds a whirling can in its circular path breaks, what kind of force causes it to move in a straight- line path: centripetal, centrifugal, or no force? What law of physics supports your answer?

No force; Newton's first law.

How can gravity be simulated in an orbiting space station?

Rotate a cylinder to create centrifugal force as viewed by a person on the inside of the curved outer wall, Spin a station shaped like a bicycle wheel, Spin two pods connected by a cable. (All of the above)

The front wheels of a racing vehicle are located far out in front to help keep the vehicle from nosing upward when it accelerates. What physics concepts play a role here?

Rotational inertia and torque are most predominantly illustrated here, and the conservation of angular momentum also plays a role. The long distance to the front wheels increases the rotational inertia of the vehicle relative to the back wheels and also increases the lever arm of the front wheels without appreciably adding to the vehicle's weight. As the back wheels are driven clockwise, the chassis tends to rotate counterclockwise (conservation of angular momentum) and thereby lift the front wheels off the ground. The greater rotational inertia and the increased clockwise torque of the more distant front wheels counter this effect.

If you hang at rest by your hands from a long vertical rope, where is your center of gravity with respect to the rope?

Somewhere straight below where your hands grab the rope.

Dan and Sue cycle at the same speed. The tires on Dan's bike are larger in diameter than those on Sue's bike. Which wheels, if either, have the greater rotational speed?

Sue's wheels have the greater rotational speed.

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

The bowling ball wins. A solid sphere of any mass and size beats both a solid cylinder and a hollow ball of any mass and size. That's because a solid sphere has less rotational inertia per mass than the other shapes. A solid sphere has the bulk of its mass nearer the rotational axis that extends through its center of mass, whereas a cylinder or hollow ball has more of its mass farther from the axis. The object with the least rotational inertia per mass is the "least lazy" and will win races.

Where is the center of mass of a baseball? Where is its center of gravity?

The center of mass and the center of gravity are both at the center of the spherical ball.

Is it an inward force or an outward force that is exerted on the clothes during the spin cycle of an automatic washing machine? What about the direction of the force on the water?

The force is inward on the clothes, and there is none on the water.

The diameter of the base of a tapered drinking cup is 6.8 cm . The diameter of its mouth is 8.0 cm . The path of the cup curves when you roll it on the top of a table. Which end, the base or the mouth moves faster? How much faster?

The mouth. 1.2

If you are not wearing a seat belt in a car that rounds a curve, and you slide across your seat and slam against a car door, what kind of force is responsible for your slide: centripetal, centrifugal, or no force?

There is no force as to someone who is viewing outside the car. To them you are moving in a straight line.

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

They are equal in magnitude and opposite in direction.

What does a torque tend to do to an object?

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

When you whirl a can at the end of a string in a circular path, what is the direction of the force you exert on the can?

Toward the center of the circle.