Conceptual Physics

Paul G. Hewitt

Chapter 8

Rotational Motion - all with Video Answers

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Chapter Questions

Problem 1

An object is executing circular motion. What is the direction of instantaneous linear speed?

Lisa Tarman

Lisa Tarman

Numerade Educator

Problem 2

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

Kara Merfeld

Numerade Educator

Problem 3

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?

Lisa Tarman

Numerade Educator

Problem 4

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?

Kara Merfeld

Numerade Educator

Problem 5

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

Lisa Tarman

Numerade Educator

Problem 6

Can two objects have the same inertia but a different moment of inertia?

Kara Merfeld

Numerade Educator

Problem 7

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

Lisa Tarman

Numerade Educator

Problem 8

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.

Kara Merfeld

Numerade Educator

Problem 9

Which is easier to get swinging: a baseball bat held at the narrow end or a bat held closer to the massive end (choked up)?

Lisa Tarman

Numerade Educator

Problem 10

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

Kara Merfeld

Numerade Educator

Problem 11

An object is rolling down an incline, what is the relationship between its acceleration and its rotational inertia?

Lisa Tarman

Numerade Educator

Problem 12

How is torque similar to force?

Kara Merfeld

Numerade Educator

Problem 13

When does a force produce zero torque?

Lisa Tarman

Numerade Educator

Problem 14

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

Kara Merfeld

Numerade Educator

Problem 15

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

Lisa Tarman

Numerade Educator

Problem 16

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

Kara Merfeld

Numerade Educator

Problem 17

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

Lisa Tarman

Numerade Educator

Problem 18

Is the center of mass of an irregularly shaped body its geometric center?

Kara Merfeld

Numerade Educator

Problem 19

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

Lisa Tarman

Numerade Educator

Problem 20

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

Kara Merfeld

Numerade Educator

Problem 21

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?

Lisa Tarman

Numerade Educator

Problem 22

When you whirl a can tied at the end of a string in a circular path, why do you need to keep pulling on the string? What is the role of the string?

Kara Merfeld

Numerade Educator

Problem 23

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

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 24

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?

Kara Merfeld

Numerade Educator

Problem 25

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”?

Melissa Walsh

Numerade Educator

Problem 26

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

Kara Merfeld

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Problem 27

How can gravity be simulated in an orbiting space station?

Lisa Tarman

Numerade Educator

Problem 28

How is angular momentum related to inertia?

Kara Merfeld

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Problem 29

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

Lisa Tarman

Numerade Educator

Problem 30

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?)

Kara Merfeld

Numerade Educator

Problem 31

Contact Grandpa and tell him how you’re learning to distinguish between closely related concepts, using the examples of force and torque. Tell him how the two are similar and how they differ. Suggest where he can find “hands-on” things in his home to illustrate the difference between the two. Also cite an example that shows how the net force on an object can be zero while the net torque isn’t, as well as an example of the other way around. (Now make your Grandpa’s day and send an actual letter to him!)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 32

Fasten a pair of foam cups together at their wide ends and roll them along a pair of meter sticks that simulate railroad tracks. Note how they self-correct whenever their path departs from the center. Question: If you taped the cups together at their narrow ends, so they tapered oppositely as shown, would the pair of cups self-correct or self-destruct when rolling slightly off center?

Miguel Perez

Numerade Educator

Problem 33

Fasten a fork, spoon, and wooden match together as shown in the sketch. The combination will balance nicely—on the edge of a glass, for example. This happens because the center of gravity actually “hangs” below the point of support.

Salamat Ali

Numerade Educator

Problem 34

Stand with your heels and back against a wall and try to bend over and touch your toes. You’ll find that you have to stand away from the wall to do so without toppling over. Compare the minimum distance of your heels from the wall with the distance for a friend of the opposite sex. Who can touch their toes with their heels nearer to the wall: men or women? On the average and in proportion to height, which sex has the lower center of gravity?

Kara Merfeld

Numerade Educator

Problem 35

First ask a friend to stand facing a wall with her toes touching the wall. Then ask her to stand on the balls of her feet without toppling backward. Your friend won’t be able to do it. Now you explain why it can’t be done.

Lisa Tarman

Numerade Educator

Problem 36

Rest a meter stick on two extended forefingers as shown. Slowly bring your fingers together. At what part of the stick do your fingers meet? Can you explain why this always happens, no matter where you start your fingers?

Kara Merfeld

Numerade Educator

Problem 37

Place the hook of a wire coat hanger over your finger. Carefully balance a coin on the straight wire on the bottom directly under the hook. You may have to flat- ten the wire with a hammer or fashion a tiny platform with tape. With a surprisingly small amount of practice you can swing the hanger and
balanced coin back and forth and then in a circle. Centripetal force holds the coin in place.

Salamat Ali

Numerade Educator

Problem 38

Torque $=$ lever arm $\times$ force

Calculate the torque produced by a 100-N perpendicular force at the end of a 0.3-m-long wrench.

Kara Merfeld

Numerade Educator

Problem 39

Torque $=$ lever arm $\times$ force

How does the torque produced change if the force reduces to 50 N while keeping the length of the wrench unchanged?

Lisa Tarman

Numerade Educator

Problem 40

Centripetal force: $F=m v^{2} / r$

A horizontal string whirls a 1-kg can in a circle of radius 2 m with a speed of 2 m/s. Calculate the tension in the string.

Kara Merfeld

Numerade Educator

Problem 41

Centripetal force: $F=m v^{2} / r$

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.

Lisa Tarman

Numerade Educator

Problem 42

Angular momentum $=m v r$

Calculate the angular momentum of the whirling can in problem 40.

Kara Merfeld

Numerade Educator

Problem 43

Angular momentum $=m v r$

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

Lisa Tarman

Numerade Educator

Problem 44

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?

Kara Merfeld

Numerade Educator

Problem 45

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?

Lisa Tarman

Numerade Educator

Problem 46

The rock and meter stick 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?

Kara Merfeld

Numerade Educator

Problem 47

In one of the photos at the beginning of this chapter, Mary Beth uses a torque feeler that consists of a meter stick 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?

Lisa Tarman

Numerade Educator

Problem 48

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.

a. Write the equation for centripetal force, and substitute the values T and L appropriately. Then, with a bit of elementary algebra, rearrange the equation so that it solves for mass.
b. Show that the mass of the puck is 5 kg when the length of the string is 2 m, the string tension is 10 N, and the tangential speed of the puck is 2 m/s.

Kara Merfeld

Numerade Educator

Problem 49

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?

Sheh Lit Chang

University of Washington

Problem 50

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 0.33 L?
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?

Kara Merfeld

Numerade Educator

Problem 51

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).

Lisa Tarman

Numerade Educator

Problem 52

Three types of rollers are placed on slightly inclined parallel meter stick tracks as shown. From greatest to least, rank the rollers in terms of their ability to remain stable as they roll.

Supratim Pal

Numerade Educator

Problem 53

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.

Linda Winkler

Numerade Educator

Problem 54

You hold a meter stick 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.

Kara Merfeld

Numerade Educator

Problem 55

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.

Samuel Smith

Numerade Educator

Problem 56

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?

Kara Merfeld

Numerade Educator

Problem 57

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?

Lisa Tarman

Numerade Educator

Problem 58

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.

Kara Merfeld

Numerade Educator

Problem 59

The wheels of railroad trains are tapered, a feature especially important on curves. How, if at all, does the amount of taper relate to how great the sharpness of curves can be?

Lisa Tarman

Numerade Educator

Problem 60

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?

Kara Merfeld

Numerade Educator

Problem 61

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?

Lisa Tarman

Numerade Educator

Problem 62

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

Kara Merfeld

Numerade Educator

Problem 63

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

Lisa Tarman

Numerade Educator

Problem 64

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?)

Kara Merfeld

Numerade Educator

Problem 65

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

Lisa Tarman

Numerade Educator

Problem 66

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.

Kara Merfeld

Numerade Educator

Problem 67

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?

Lisa Tarman

Numerade Educator

Problem 68

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

Kara Merfeld

Numerade Educator

Problem 69

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?

Lisa Tarman

Numerade Educator

Problem 70

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

Kara Merfeld

Numerade Educator

Problem 71

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

Lisa Tarman

Numerade Educator

Problem 72

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

Kara Merfeld

Numerade Educator

Problem 73

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

Lisa Tarman

Numerade Educator

Problem 74

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

Kara Merfeld

Numerade Educator

Problem 75

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

Lisa Tarman

Numerade Educator

Problem 76

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

Kara Merfeld

Numerade Educator

Problem 77

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

Lisa Tarman

Numerade Educator

Problem 78

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

Kara Merfeld

Numerade Educator

Problem 79

The centers of gravity of the three trucks parked on a hill are shown by the X s. Which truck(s) will tip over?

Lisa Tarman

Numerade Educator

Problem 80

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?

Kara Merfeld

Numerade Educator

Problem 81

An object is moving with constant speed in a circular path. Is a force acting on it?

Lisa Tarman

Numerade Educator

Problem 82

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

Kara Merfeld

Numerade Educator

Problem 83

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?

Sheh Lit Chang

University of Washington

Problem 84

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.)

Kara Merfeld

Numerade Educator

Problem 85

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

Lisa Tarman

Numerade Educator

Problem 86

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

Kara Merfeld

Numerade Educator

Problem 87

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.

Lisa Tarman

Numerade Educator

Problem 88

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.

Kara Merfeld

Numerade Educator

Problem 89

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 horizontal red vector represent the normal force acting on the bike and rider, the centripetal force, both, or neither? Defend your answer.

Sheh Lit Chang

University of Washington

Problem 90

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?

Kara Merfeld

Numerade Educator

Problem 91

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?

Lisa Tarman

Numerade Educator

Problem 92

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 the radial direction of the ball’s circular path. (Yes, the normal is appreciably greater than the weight!)

Kara Merfeld

Numerade Educator

Problem 93

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.)

Lisa Tarman

Numerade Educator

Problem 94

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?

Kara Merfeld

Numerade Educator

Problem 95

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?

Sheh Lit Chang

University of Washington

Problem 96

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?

Kara Merfeld

Numerade Educator

Problem 97

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?

Lisa Tarman

Numerade Educator

Problem 98

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.

Kara Merfeld

Numerade Educator

Problem 99

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.

Sheh Lit Chang

University of Washington

Problem 100

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

Kara Merfeld

Numerade Educator

Problem 101

An automobile speedometer is configured to read speed proportional to the rotational speed of its wheels. If the oversize 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.

Salamat Ali

Numerade Educator

Problem 102

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).

Kara Merfeld

Numerade Educator

Problem 103

In this chapter, we learned that an object may not be in mechanical equilibrium even when $\Sigma F=0.$ Discuss what else defines mechanical equilibrium.

Salamat Ali

Numerade Educator

Problem 104

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.)

Kara Merfeld

Numerade Educator

Problem 105

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

Salamat Ali

Numerade Educator

Problem 106

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

Kara Merfeld

Numerade Educator

Problem 107

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

Salamat Ali

Numerade Educator

Problem 108

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

Kara Merfeld

Numerade Educator

Problem 109

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?

Salamat Ali

Numerade Educator

Problem 110

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.

Kara Merfeld

Numerade Educator

Problem 111

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.

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 112

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.)

Kara Merfeld

Numerade Educator

Problem 113

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?

Salamat Ali

Numerade Educator

Problem 114

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.

Kara Merfeld

Numerade Educator

Problem 115

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.)

Michael Sorola

Numerade Educator

Problem 116

Most often we say that force causes acceleration. But when Evan took a ride in a rocket sled at Bonneville Salt Flats, blood was forced to the back of his brain, nearly blacking him out. Discuss and identify the cause of this force.

Kara Merfeld

Numerade Educator