Chapter Questions
A figure skater is spinning with her arms held straight out. Which has greater rotational speed, her shoulders or her fingertips? Why?
Who has the greater rotational speed, a person living on the equator or one living in New York City?
Drew and Blake are riding on a merry-go-round at the county fair. Drew is riding near the center while Blake is near the outside. Compare their rotational accelerations.
You are looking down on a meny-go-round and observe that it is rotating clockwise. What is the direction of the merry-go-round's rotational velocity? If the merrygo-round is slowing down, what is the direction of its rotational acceleration?
What is the direction of the rotational velocity of Earth?
Earth's rotational speed is slowing because of the tidal influences of the Sun and Moon. What is the direction of Earth's rotational acceleration?
What happens to the surface area of a cube when the length of each side is doubled? How does this compare with what happens to the surface area of a sphere when you double its radius?
What is needed to change the rotational velocity of an object?
Future space stations will rotate to produce artificial gravity. What torque (if any) is needed to keep the space stations rotating?
A flywheel with a large rotational inertia is often attached to the drive shaft of automobile engines. What purpose does the flywheel serve?
If the object shown in the following figure is fixed but free to rotate about point $A,$ which force will produce the larger torque? Why?
If the object shown in the preceding figure is not fixed and point $A$ is the object's center of mass, which force will produce translational motion without rotation?
Use the concept of torque to explain how a claw hammer is used to pull nails.
Apply the concept of torque to explain how a wheelbarrow allows you to transport a heavy load with a lifting force much less than the weight of the load.
You are a window washer and, rather than use the fancy lift, you decide just to lean a ladder up against a large plate glass window. Use the concept of torque to explain why the likelihood of breaking the ylass increases the higher you climb up the ladder.
A 10 -speed bicycle has five gears on the rear wheel. When the bicycle is in first gear, is the chain on the gear with the largest radius or the smallest radius? Use the concept of torque to explain your answer.
Sam and Kelly are carrying an office desk. Sam has to exert a much greater force than Kelly does to keep the desk level. Is the desk's center of mass closer to Sam or to Kelly? Use the concept of torque to justify your answer.
Dana and Loren are carrying a steel girder. As shown in the following figure, Dana is holding the girder at the end while Loren is not. Who is exerting the greater force on the girder? Justify your answer using the concept of torque.
Two flywheels have the same mass, but one has a radius twice that of the other. If both flywheels are spinning about their axes at the same rate, which one would be harder to stop? Why?
Which would be harder to rotate about its center, a 12 foot-long $2^{\prime \prime} \times 4^{\prime \prime}$ board or a 6 -foot-long $4^{\circ} \times 4^{\prime \prime}$ board? Why?
Does an object's rotational inertia increase or decrease with a uniform increase in mass? Does it increase or decrease as the mass is moved closer to the axis of rotation?
Would you have a larger rotational inertia in the tuck, pike, or layout position? Why? (See Figure $8-16$ if you are not familiar with these diving positions.)
A solid sphere and a solid cylinder are made of the same material. If they have the same mass and radius, which one has the smaller rotational inertia about its center? Why?
If a solid disk and a hoop have the same mass and radius, which would have the smaller rotational inertia about its center of mass? Why?
Earth spins about its own axis once every 23 hours and 56 minutes. Why has this rate changed very little since the time of Isaac Newton?
Find an everyday example that clearly illustrates the meaning of Newton's second law for rotation.
In the text we found the center of mass at the intersection of two lines. If you suspend the object from a third point, this line passes through the intersection of the first two. Why?
Where is the center of mass of the figurine resting on the pedestal in the following figure?
A spoon and a fork can be suspended beyond the edge of a glass by using a flat toothpick, as shown in the following figure. Where is the center of mass of the spoon-fork combination?
Using diagrams, show why an empty ice cream cone is more stable when it is placed upside down rather than on its tip.
The Leaning Tower of Pisa is stable even though it is tilted significantly from the vertical. If a greedy developer decided to add three more stories to this historical landmark, it might well topple over. Use the concept of stable equilibrium to explain this.
A marble is resting in a round bowl. Is the marble in stable or unstable equilibrium? Why?
The Pacific Science Center in Seatile, Washington, has an exhibit in which patrons can ride a bicycle around a narrow track high above the ground. A large concrete block hangs beneath the bike on a long bar that is fastened rigidly to the bike's frame. The following picture shows Greg's wife Sandra riding the bike without much concern for her safety. Why is this exhibit safe?
If you stand with your back against the wall and try to bend over and touch your toes, you will invariably tip over. Use the concept of equilibrium to explain why,
If you stand facing a wall with your toes touching the wall, you cannot raise yourself up on your tiptoes. Use the concept of equilibrium to explain why.
It is possible (and quite likely) for a high jumper's center of mass to pass under the bar while the jumper passes over the bar as shown in the following figure. Explain how this is possible.(IMAGE CAN'T COPY)
A solid cylinder and a hoop have the same mass and radius. If both are rotating with the same speed, which will have the largest rotational kinetic energy?
Suppose you race the solid cylinder and the hoop from Question 38 down a ramp. Use the concept of rotational kinetic energy to argue that the solid cylinder will reach the bottom of the ramp first.
If you are asked to design a 50 -pound flywheel for use in a new car, would you want to concentrate the mass as close as possible to the axis of rotation or as far away as possible? Explain your reasoning.
Why does a helicopter with two sets of rotors not need a rotor on the tail?(IMAGE CAN'T COPY)
A Huey helicopter has an engine failure in one of its two engines, causing the back propeller to suddenly stop rotating. What happens to the helicopter? Use the concept of conservation of angular momentum to explain your answer.
In which of the following positions would a diver have the smallest rotational inertia for performing a front somersault: tuck, pike, or layout? Why? (See Figure 8-16 if you are not familiar with these diving positions.)
Why is it possible for a high diver to execute more front somersaults in the tuck position than in the layout position?
Why do figure skaters spin faster when they pull in their arms?(IMAGE CAN'T COPY)
An astronaut "Iloating" in a space shuttle has an initial rotational motion but no initial translational motion relative to the shutile. Why does the astronaut continue to rotate?(IMAGE CAN'T COPY)
A cat that is held upside down and dropped with no initial angular momentum manages to land on its feet. Does the cat need to acquire any angular momentum to do this? Explain your reasoning.
A common early maneuver learned on a trampoline is to land sitting with your feet pointing in one direction and to then reverse directions on the bounce to land with your feet pointing in the opposite direction. With practice it is possible to turn either direction on command afler leaving the mat. How is this possible?
If you look down the inside of the barrel of a rifle, you see long spiral grooves. When the bullet travels down the barrel, these grooves cause the bullet to spin. Why would we want the bullet to spin?
A billiard ball without spin hits perpendicular to the cushion and bounces back perpendicular to the cushion. However, if the ball is spinning about the vertical, it bounces off to one side and spins at a slower rate. What is the force that causes the change (a) in the ball's linear momentum? (b) In its angular momentum?
Figure $6-4$ shows a fire extinguisher being used to propel a person in a straight line. A fire extinguisher could also be used to turn a merry-go-round if a person were to sit on one of the horses and fire the extinguisher backward. As it speeds up, the merry go-round acquires angular momentum. Use the concept of torque to account for this change in angular momentum.
An air-hockey puck is whirling on the end of a string that passes through a small hole in the center of the table, as shown in the following figure. What happens to the speed of the puck as the string is slowly pulled down through the hole?(IMAGE CAN'T COPY)
A gyroscope that points horizontally at the North Pole is transported to the South Pole while it continues to spin. Which way does it point? Explain.
A gyroscope is oriented so that it points toward the North Star when it is in Seattle. If it is carried to the equator while it continues to spin, which way will it point, and why?
Some people have proposed powering cars by extracting energy from large rotating flywheels mounted in the car. There is a problem with this suggestion if only one flywheel is used. What is the problem and how can it be remedied?
The film crew of Candid Camera replaces a person's briefcase with an identical one that contains a mounted and spinning flywheel. Explain what happens when the person tries to carry the briefcase around a comer.
A teacher sits on a stool that is free to rotate. She holds a rotating flywheel with the axis vertical such that the wheel spins clockwise when viewed from above. She turns the wheel completely over, and she begins to spin on the stool. Does she spin clockwise or counterclockwise? Justify your answer using the concept of conservation of angular momentum.
The rotational axis of Farth's spin is tilted $28 \frac{1}{2}$ degrees relative to Earth's axis of revolution about the Sun. The North Pole is tilted toward the Sun on June $22 .$ Which pole is tilted toward the Sun on December $22 ?$
If you stand outside all night and watch the stars, they all appear to move except one. Which star appears to remain stationary, and why?
Why is the star Polaris not always located directly above Farth's geographic North Pole?
You jump onto a merry-go-round that is rotating clockwise as vicwed from above. Find the direction of (a) the merry-go-round's angular momentum, (b) the merrygo-round's change in angular momentum, (c) your change in angular momentum, and (d) the change in angular momentum for the system made up of you and the merry-go-round. Assume that the merry go-round has very good bearings.
As you walk from the center of a merry-go-round toward the outer edge, the merry-go-round slows. Is angular momentum conserved? Explain why or why not.
If the beaters on a food mixer make 1000 revolutions in 5 min, what is the average rotational speed of the beaters? Fxpress your answer in both revolutions per minute and revolutions per second.
If a CD makes 1500 revolutions in 5 min, what is the CD's average rotational speed?
What is the rotational speed of the hand on a clock that measures the minutes?
What is the rotational speed of the hand on a clock that measures the seconds?
If it takes 3 s for a modern DVD player to stop a DVD with a rotational speed of 7490 rpm, what is the DVD's average rotational acceleration?
A variable-speed drill, initially turning at $400 \mathrm{rpm}$, speeds "p to 1000 rpm in 0.5 s. What is its average rotational acceleration?
What torgue does a $140-\mathrm{N}$ salmon exert about the handle of a 1.5 -m-long fishing pole if the pole is horizontal and the salmon is out of the water?
You are holding a $5-\mathrm{k} q$ dumbbell straight out at arm's length. Assuming that your arm is $0.70 \mathrm{m}$ long, and that your shoulder acts as a pivot, what torque is the dumbbell exerting?
A pirate with a mass of $90 \mathrm{kg}$ stands on the end of a plank that extends $2 \mathrm{m}$ beyond the gunwale. What torque does he exert on the plank?
Robin is standing terrified at the end of a diving board, which is high above the water. If Robin has a mass of 65 $\mathrm{kg}$ and is standing $1.5 \mathrm{m}$ from the board's pivot point, what torque is Robin exerting on the board?
Two children with masses of $20 \mathrm{kg}$ and $30 \mathrm{kg}$ are sitting on a balanced seesaw. If the lighter child is sitting $3 \mathrm{m}$ from the center, where is the heavier child sitting?
A child with a mass of $20 \mathrm{kg}$ sits at a distance of $2 \mathrm{m}$ from the pivot point of a seesaw. Where should a 14 -kg child sit to balance the seesaw?
Is the system shown in the following figure balanced? If not, which end will fall? Explain your reasoning.(IMAGE CAN'T COPY)
What mass would you liang on the right side of the system in the following figure to balance it- - that is, to make the clockwise and counterclockwise torques equal?(IMAGE CAN'T COPY)
Cliff and Will are carrying a uniform 2.0 -m board of mass71 kq. Will is supporting the board at the end while Cliff is $0.6 \mathrm{m}$ from the other end as shown in the following figure. Cliff has attached his lunch to his end of the board, and the tension in the string supporting the lunch is 200N. Draw an extended free-body diagram for the board, and find the forces exerted by Cliff and Will.(IMAGE CAN'T COPY)
Two construction workers, Cliff and Will, are holding a triangular pane of glass as shown in the following figure. The weight of the glass is $300 \mathrm{N}$. The center of gravity is indicated by a cross on the diagram. Both of the workers are pushing directly upward on the glass and the pane of glass is not moving. Draw an extended free-body diagram for the pane of glass, and find the forces exerted by Cliff and will.
A child with a mass of $50 \mathrm{kg}$ is riding on a merry-goround. If the child has a speed of $3 \mathrm{m} / \mathrm{s}$ and is located$2 \mathrm{m}$ from the center of the merry-go-round, what is the child's angular momentum?
A $1600-\mathrm{kg}$ car is traveling at $20 \mathrm{m} / \mathrm{s}$ around a curve witha radius of $120 \mathrm{m}$. What is the angular momentum of the car?
Which has the larger angular momentum about the Sun, Mars or Earth? The radius, speed, and mass of Mars are $1.5,0.8,$ and 0.11 times those of Earth, respectively.
Mercury follows an elliptical orbit that takes it as close as 46 million km to the Sun and as far as 70 million km from the Sun. At both of these locations, Mercury's velocity makes a right angle to the direction to the Sun. If Mercury's speed is $38 \mathrm{km} / \mathrm{s}$ when it is farthest from the Sun, how fast is it moving when it is closest to the Sun?