Mary Beth uses a torque feeler that consists of a meter-

What are the units of measurement for tangential speed? For rotational speed?

On a rotating turntable, does tangential speed or rotational speed vary with distance from the center?

A tapered cup rolled on a flat surface makes a circular path. What does this tell you about the tangential speed of the rim of the wide end of the cup compared with that of the rim of the narrow end?

What is rotational inertia, and how is it similar to inertia as studied in earlier chapters?

How does the tapered rim of a wheel on a railroad train allow one part of the rim to have a greater tangential speed than another part when it is rolling on a track?

Inertia depends on mass; rotational inertia depends on mass and something else. What?

As distance increases between most of the mass of an object and its center of rotation, does rotational inertia increase or decrease?

Consider three axes of rotation for a pencil: along the lead, at right angles to the lead at the middle, and at right angles to the lead at one end. Rate the rotational inertias about each axis from smallest to largest.

Why does bending your legs when running enable you to swing your legs to and fro more rapidly?

Which will have the greater acceleration rolling down an incline: a hoop or a solid disk?

What does a torque tend to do to an object?

What is meant by the “lever arm” of a torque?

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

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

Where is the center of mass of a baseball? Where is its center of gravity? Where are these centers for a baseball bat?

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

Where is the center of mass of a hollow soccer ball?

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

In terms of center of gravity, support base, and torque, 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?

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

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?

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

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?

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? Why is the correct answer “no force”?

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

Distinguish between linear momentum and angular momentum.

How can gravity be simulated in an orbiting space station?

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

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 increase? (Why do your answers differ?)

Calculate the torque produced by a 50-N perpendicular force at the end of a \(0.2-m\)-long wrench. Equation Transcription: Text Transcription: 0.2-m

Calculate the torque produced by the same \(50-N\) force when a pipe extends the length of the wrench to \(0.5 m\). Equation Transcription: Text Transcription: 50-N 0.5 m

Calculate the tension in a horizontal string that whirls a \(2-kg\) toy in a circle of radius \(2.5 m\) when it moves at \(3 m/s\) on an icy surface. Equation Transcription: Text Transcription: 2-kg 2.5 m 3 m/s

Calculate the angular momentum of the person in the preceding problem.

Calculate the force of friction that keeps an 80-kg person sitting on the edge of a horizontal rotating platform when the person sits 2 m from the center of the platform and has a tangential speed of 3 m/s. Angular momentum = mvr

If a person’s speed doubles and all else remains the same, what will be the person’s angular momentum?

The diameter of the base of a tapered drinking cup is \(6 cm\). The diameter of its mouth is \(9 cm\). The path of the cup curves when you roll it on the top of a table. Which end, the base or the mouth, rolls faster? How much faster? Equation Transcription: Text Transcription: 6 cm 9 cm

To tighten a bolt, you push with a force of 80 N at the end of a wrench handle that is 0.25 m from the axis of the bolt. a. What torque are you exerting? b. You move your hand inward to be only 0.10 m from the bolt. To achieve the same torque, show that you should exert 200 N of force. c. Do your answers depend on the direction of your push relative to the direction of the wrench handle?

The rock and meterstick balance at the \(25-cm\) mark, as shown in the sketch. The meter stick has a mass of \(1 kg\). What must be the mass of the rock? Equation Transcription: Text Transcription: 25-cm 1 kg

In one of the photos at the beginning of this chapter, Mary Beth uses a torque feeler that consists of a meterstick held at the 0-cm end with a weight dangling from various positions along the stick. When the stick is held horizontally, torque is produced when a 1-kg object hangs from the 50-cm mark. How much more torque is exerted when the object is hung from the 75-cm mark? The 100-cm mark?

An ice puck of mass m revolves on an icy surface in a circle at speed \(v\) at the end of a horizontal string of length \(L\). The tension in the string is \(T\). Equation Transcription: Text Transcription: v L T

If a trapeze artist rotates once each second while sailing through the air and contracts to reduce her rotational inertia to one-third of what it was, how many rotations per second will result?

A small space telescope at the end of a tether line of length L moves at linear speed v about a central space station. a. What will be the linear speed of the telescope if the length of the line is reduced to 0.33L? b. If the initial linear speed of the telescope is 1.0 m/s, what is its speed when pulled in to one-third its initial distance from the space station?

The three cups are rolled on a level surface. Rank the cups by how far they depart from a straight-line path (most curved to least curved).

Beginning from a rest position, a solid disk A, a solid ball B, and a hoop C race down an inclined plane. Rank them in reaching the bottom: winner, second place, and third place.

You hold a meterstick at one end with the same mass suspended at the opposite end. Rank the torque needed to keep the stick steady, from largest to smallest.

Three physics majors in good physical shape stand with their backs against a wall. Their task is to lean over and touch their toes without toppling over. Rank their chances for success from highest to lowest.

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?

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?

Use the equation \(v=r \omega\) to explain why the end of a flyswatter moves much faster than your wrist when you swat a fly. Text Transcription: v = r omega

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?

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

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?

A softball and a basketball start from rest and roll down an incline. Which ball reaches the bottom first? Defend your answer.

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?)

Can a force produce a torque when there is no lever arm?

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.

When the line of action of a force intersects the center of mass of an object, can that force produce a torque about the object’s center of mass?

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

Why does sitting closest to the center of a vehicle provide the most comfortable ride in a bus traveling on a bumpy road, in a ship in a choppy sea, or in an airplane in turbulent air?

Explain why a long pole is more beneficial to a tightrope walker if the pole droops.

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

Why is the wobbly motion of a single star an indication that the star has one or more planets orbiting around it?

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

Where is the center of mass of Earth’s atmosphere?

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

Why is it important to secure file cabinets to the floor, especially cabinets with heavy loads in the top drawers?

Describe the comparative stabilities of the three objects shown in terms of work and potential energy.

The centers of gravity of the three trucks parked on a hill are shown by the \(Xs\). Which truck(s) will tip over? Equation Transcription: Text Transcription: Xs

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?

Can an object move along a curved path if no force acts on it? Defend your answer.

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

When you are in the front passenger seat of a car turning to the left, you may find yourself pressed against the right-side door. Why do you press against the door? Why does the door press on you? Does your explanation involve a centrifugal force or Newton’s laws?

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? (Hint: Consider vector components of the normal force on the car.)

Under what conditions could a fast-moving car remain on a banked track covered with slippery ice?

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

The sketch shows a coin at the edge of a turntable. The weight of the coin is shown by the vector \(W\). Two other forces act on the coin—the normal force and a force of friction that prevents it from sliding off the edge. Draw force vectors for both of these. Equation Transcription: Text Transcription: W

The occupant inside a rotating space habitat of the future feels that she is being pulled by artificial gravity against the outer wall of the habitat (which becomes the “floor"). Explain what is going on in terms of Newton’s laws and centripetal force.

A motorcyclist is able to ride on the vertical wall of a bowl-shaped track as shown. Friction of the wall on the tires is shown by the vertical red vector. (a) How does the magnitude of this vertical vector compare with the weight of the motorcycle and rider? (b) Does the hori- zontal red vector represent the normal force acting on the bike and rider, the centripetal force, both, or neither? Defend your answer.

The sketch shows a conical pendulum. The bob swings in a circular path. The tension T and weight W are shown by vectors. Draw a parallelogram with these vectors, and show that their resultant lies in the plane of the circle. (See the parallelogram rule in Chapter 2.) What is the name of this resultant force?

You sit at the middle of a large turntable at an amusement park as it is set spinning and then allowed to spin freely. When you crawl toward the edge of the turntable, does the rate of the rotation increase, decrease, or remain unchanged? What physics principle supports your answer?

Consider a ball rolling around in a circular path on the inner surface of a cone. The weight of the ball is shown by the vector W. Without friction, only one other force acts on the ball—a normal force. (a) Draw in the vector for the normal force. (The length of the vector depends on the next step, b.) (b) Using the parallelogram rule, show that the resultant of the two vectors is along

A sizable quantity of soil is washed down the Mississippi River and deposited in the Gulf of Mexico each year. What effect does this tend to have on the length of a day? (Hint: Relate this to Figure 8.52.)

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?

Strictly speaking, as more and more skyscrapers are built on the surface of Earth, does the day tend to become longer or shorter? And, strictly speaking, does the falling of autumn leaves tend to lengthen or shorten the 24-hour day? What physics principle supports your answers?

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?

If the polar ice caps on Earth’s solid surface were to melt, the oceans would be deeper. Strictly speaking, what effect would this have on Earth’s rotation?

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.

We believe that our galaxy was formed from a huge cloud of gas. The original cloud was far larger than the present size of the galaxy, was more or less spherical, and was rotating much more slowly than the galaxy is now. In this sketch, we see the original cloud and the galaxy as it is now (seen edgewise). Explain how the inward pull of gravity and the conservation of angular momentum contribute to the galaxy’s present shape and why it rotates faster now than when it was a larger, spherical cloud.

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

An automobile speed ometer is configured to read speed proportional the rotational speed of its wheels. If the over size wheels of this red car were installed with out making speedometer corrections, discuss whether the speedometer reading will be high, or low—or no change.

A large wheel is coupled to a wheel with half the diameter, as shown in the sketch. How does the rotational speed of the smaller wheel compare with that of the larger wheel? Discuss the comparisons of the tangential speeds at the rims (assuming the belt doesn’t slip).

In this chapter, we learned that an object may not be in mechanical equilibrium even when \(\sum F=0\). Discuss what else defines mechanical equilibrium. Text Transcription: sum F=0

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. (Consider the time that the unbalanced torque acts.)

Discuss why a car noses up when accelerating and noses down when braking.

Discuss how a ramp would help you to distinguish between two identical-looking spheres of the same weight, one solid and the other hollow.

Which will roll down an incline faster: a can of water or a can of ice? Discuss and explain.

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

A youngster who has entered a soapbox derby (in which four-wheel, unpowered vehicles roll from rest down a hill) asks if large massive wheels or lightweight ones should be used. Also, should the wheels have spokes or be solid? What advice do you offer?

The spool is pulled in three ways, as shown. There is sufficient friction for rotation. In what direction will the spool roll in each case? Discuss and explain.

Nobody at the playground wants to play with the obnoxious boy, so he fashions a seesaw as shown so he can play without anyone else. Discuss how this is done.

How can the three bricks be stacked so that the top brick has maximum horizontal displacement from the bottom brick? For example, stacking them as suggested by the dashed lines would be unstable and the bricks would topple. (Hint: Start with the top brick and work down. At every interface the CG of the bricks above must not extend beyond the end of the supporting brick.)

A long track balanced like a seesaw supports a golf ball and a more massive billiard ball with a compressed spring between the two. When the spring is released, the balls move away from each other. Does the track tip clockwise, tip counterclockwise, or remain in balance as the balls roll outward? What principles do you use for your discussion and explanation?

With respect to Diana’s finger, where is the center of mass of the plastic bird? Discuss how this balance can be accomplished during its manufacture.

When a long-range cannonball is fired toward the equator from a northern (or southern) latitude, it lands west of its “intended” longitude. Discuss why this is so. (Hint: Consider a flea jumping from partway out to the outer edge of a rotating turntable.)