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physics
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Physics 5th edition James S. Walker - Solutions

The Earth's rate of rotation is constantly decreasing, causing the day to increase in duration. In the year 2006 the Earth took about 0.840 s longer to complete 365 revolutions than it did in the year 1906. What was the average angular acceleration, in rad/s2, of the Earth during this time?
When a carpenter shuts off his circular saw, the 10.0-inchdiameter blade slows from 3984 rpm to 0 in 1.25 s.(a) What is the angular acceleration of the blade?(b) What is the distance traveled by a point on the rim of the blade during the deceleration?(c) What is the magnitude of the net
The drill used by most dentists today is powered by a small air turbine that can operate at angular speeds of 350,000 rpm. These drills, along with ultrasonic dental drills, are the fastest turbines in the world-far exceeding the angular speeds of jet engines. Suppose a drill starts at rest and
Two children, Jason and Betsy, ride on the same merry-go-round. Jason is a distance R from the axis of rotation; Betsy is a distance 2R from the axis.(a) Is the rotational period of Jason greater than, less than, or equal to the rotational period of Betsy?(b) Choose the best explanation from among
The hour hand on a certain clock is 8.2 cm long. Find the tangential speed of the tip of this hand.
The outer edge of a rotating Frisbee with a diameter of 29 cm has a linear speed of 3.7 m/s. What is the angular speed of the Frisbee?
A carousel at the local carnival rotates once every 45 seconds.(a) What is the linear speed of an outer horse on the carousel, which is 2.75 m from the axis of rotation?(b) What is the linear speed of an inner horse that is 1.75 m from the axis of rotation?
A chainsaw is shown in FIGURE 10-27. When the saw is in operation, the chain moves with a linear speed of v = 5.5 m/s. At the end of the saw, the chain follows a semicircular path with a radius of r = 0.044 m.(a) What is the angular speed of the chain as it goes around the end of the saw?(b) What
Jeff of the Jungle swings on a vine that is 7.20 m long (FIGURE 10-28). At the bottom of the swing, just before hitting the tree, Jeff's linear speed is 8.50 m/s.(a) Find Jeff's angular speed at this time.(b) What centripetal acceleration does Jeff experience at the bottom of his swing?(c) What
A compact disk, which has a diameter of 12.0 cm, speeds up uniformly from 0.00 to 4.00 rev/s in 3.00 s. What is the tangential acceleration of a point on the outer rim of the disk at the moment when its angular speed is(a) 2.00 rev/s(b) 3.00 rev/s?
Express the angular velocity of the second hand on a clock in the following units:(a) rev/h,(b) deg/min,(c) rad/s.
When a compact disk with a 12.0-cm diameter is rotating at 34.6 rad/s, what are(a) The linear speed(b) The centripetal acceleration of a point on its outer rim?(c) Consider a point on the CD that is halfway between its center and its outer rim. Without repeating all of the calculations required for
As Tony the fisherman reels in a "big one," he turns the spool on his fishing reel at the rate of 2.0 complete revolutions every second (FIGURE 10-29).(a) If the radius of the reel is 2.3 cm, what is the linear speed of the fishing line as it is reeled in?(b) How would your answer to part (a)
A Ferris wheel with a radius of 9.5 m rotates at a constant rate, completing one revolution every 36 s. Find the direction and magnitude of a passenger's acceleration when(a) At the top(b) At the bottom of the wheel.
Suppose the Ferris wheel in the previous problem begins to decelerate at the rate of 0.22 rad/s2 when the passenger is at the top of the wheel. Find the direction and magnitude of the passenger's acceleration at that time.
To polish a filling, a dentist attaches a sanding disk with a radius of 3.20 mm to the drill.(a) When the drill is operated at 2.15 × 104 rad/s, what is the tangential speed of the rim of the disk?(b) What period of rotation must the disk have if the tangential speed of its rim is to be 275 m/s?
The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the lowest-energy orbit the distance from the proton to the electron is 5.29 × 10-11 m, and the linear speed of the electron is 2.18 × 106 m/s.(a) What is the
A wheel of radius R starts from rest and accelerates with a constant angular acceleration a about a fixed axis. At what time t will the centripetal and tangential accelerations of a point on the rim have the same magnitude?
Most microwave ovens have a glass tray that sits on top of a circular ring with three small wheels, as shown in FIGURE 10-30. A small motor in the base of the microwave rotates the glass tray to provide uniform heating. When the glass tray completes one revolution, does the circular ring below it
The tires on a car have a radius of 31 cm. What is the angular speed of these tires when the car is driven at 15 m/s?
A child pedals a tricycle, giving the driving wheel an angular speed of Ï‰ = 0.875 rev/s (FIGURE 10-31). If the radius of the wheel is r = 0.260 m, what is the child's linear speed, v?
Rank the following in order of increasing angular speed: an automobile tire rotating at 2.00 × 103 deg/s, an electric drill rotating at 400.0 rev/min, and an airplane propeller rotating at 40.0 rad/s.
A soccer ball, which has a circumference of 70.0 cm, rolls 14.0 yards in 3.35 s. What was the average angular speed of the ball during this time?
You drive down the road at 31 m/s (70 mi/h) in a car whose tires have a radius of 34 cm.(a) What is the period of rotation of the tires?(b) Through what angle does a tire rotate in one second?
The wheels of a skateboard roll without slipping as it accelerates at 0.35 m/s2 down an 85-m-long hill. If the skateboarder travels at 1.8 m/s at the top of the hill, what is the average angular speed of the 2.6-cm-radius wheels during the entire trip down the hill?
The page feed roller of a computer printer grips each 11-inchlong sheet of paper and feeds it through the print mechanism. If the roller has a radius of 6.4 mm and the drive motor has a maximum angular speed of 480 rpm, what is the maximum number of pages that the printer can print each minute?
As you drive down the road at 17 m/s, you press on the gas pedal and speed up with a uniform acceleration of 1.12 m/s2 for 0.65 s. If the tires on your car have a radius of 33 cm, what is their angular displacement during this period of acceleration?
The minute and hour hands of a clock have a common axis of rotation and equal mass. The minute hand is long, thin, and uniform; the hour hand is short, thick, and uniform.(a) Is the moment of inertia of the minute hand greater than, less than, or equal to the moment of inertia of the hour hand?(b)
Suppose a bicycle wheel is rotated about an axis through its rim and parallel to its axle.(a) Is its moment of inertia about this axis greater than, less than, or equal to its moment of inertia about its axle?(b) Choose the best explanation from among the following:I. The moment of inertia is
The moment of inertia of a 0.98-kg bicycle wheel rotating about its center is 0.13 kg ∙ m2. What is the radius of this wheel, assuming the weight of the spokes can be ignored?
An electric fan spinning with an angular speed of 13 rad/s has a kinetic energy of 4.6 J. What is the moment of inertia of the fan?
Some dragonflies splash down onto the surface of a lake to clean themselves. After this dunking, the dragonflies gain altitude, and then spin rapidly at about 1000 rpm to spray the water off their bodies. When the dragonflies do this "spin-dry," they tuck themselves into a "ball" with a moment of
A spot of paint on a bicycle tire moves in a circular path of radius 0.29 m. When the spot has traveled a linear distance of 2.73 m, through what angle has the tire rotated? Give your answer in radians.
The L-shaped object in FIGURE 10-32 can be rotated in one of the following three ways: case 1, rotation about the x axis; case 2, rotation about the y axis; and case 3, rotation about the z axis (which passes through the origin perpendicular to the plane of the figure). Rank these three cases in
A 12-g CD with a radius of 6.0 cm rotates with an angular speed of 34 rad/s.(a) What is its kinetic energy?(b) If its kinetic energy is to be quadrupled, should its angular speed be doubled, quadrupled, or increased by a factor of 16?(c) Calculate the angular speed required to quadruple the kinetic
The engine of a model airplane must both spin a propeller and push air backward to propel the airplane forward.(a) Model the propeller as three 0.20-m-long thin rods of mass 0.040 kg each, with the rotation axis at one end. What is the moment of inertia of the propeller?(b) How much energy is
One way to store energy is in the rotational motion of a flywheel, and some have proposed using such technology to power automobiles. One unit is based on a 6.0-kg flywheel in the shape of a hoop of radius 0.10 m that spins as fast as 60,000 rpm.(a) How much kinetic energy is stored by the flywheel
When a pitcher throws a curve ball, the ball is given a fairly rapid spin. If a 0.15-kg baseball with a radius of 3.7 cm is thrown with a linear speed of 48 m/s and an angular speed of 42 rad/s, how much of its kinetic energy is translational and how much is rotational? Assume the ball is a
A lawn mower has a flat, rod-shaped steel blade that rotates about its center. The mass of the blade is 0.65 kg and its length is 0.55 m.(a) What is the rotational energy of the blade at its operating angular speed of 3500 rpm?(b) If all of the rotational kinetic energy of the blade could be
Consider the physical situation shown in Conceptual Example 10-18. Suppose this time a ball is released from rest on the frictionless surface. When the ball comes to rest on the no-slip surface, is its height greater than, less than, or equal to the height from which it was released?
Suppose the block in Example 10-19 has a mass of 2.1 kg and an initial upward speed of 0.33 m/s. Find the moment of inertia of the wheel if its radius is 8.0 cm and the block rises to a height of 7.4 cm before momentarily coming to rest.
Calculate the speeds of(a) The disk(b) The hoop at the bottom of the inclined plane in Conceptual Example 10-17 if the height of the incline is 0.55 m.
The two masses (m1 = 5.0 kg and m2 = 3.0 kg) in the Atwood's machine shown in FIGURE 10-33 are released from rest, with m1 at a height of 0.75 m above the floor. When m1 hits the ground its speed is 1.8 m/s. Assuming that the pulley is a uniform disk with a radius of 12 cm,(a) Outline a strategy
One of the most studied objects in the night sky is the Crab nebula, the remains of a supernova explosion observed by the Chinese in 1054. In 1968 it was discovered that a pulsar- a rapidly rotating neutron star that emits a pulse of radio waves with each revolution-lies near the center of the Crab
In Conceptual Example 10-18, assume the ball is a solid sphere of radius 2.9 cm and mass 0.14 kg. If the ball is released from rest at a height of 0.78 m above the bottom of the track on the no-slip side,(a) What is its angular speed when it is on the frictionless side of the track?(b) How high
After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of vi = 2.62 m/s (FIGURE 10-34). To reach the rack, the ball rolls up a ramp that rises through a vertical height of h = 0.47 m.(a) What is the linear speed of the ball when it reaches
A 1.3-kg block is tied to a string that is wrapped around the rim of a pulley of radius 7.2 cm. The block is released from rest.(a) Assuming the pulley is a uniform disk with a mass of 0.31 kg, find the speed of the block after it has fallen through a height of 0.50 m.(b) If a small lead weight is
After doing some exercises on the floor, you are lying on your back with one leg pointing straight up. If you allow your leg to fall freely until it hits the floor (FIGURE 10-35), what is the tangential speed of your foot just before it lands? Assume the leg can be treated as a uniform rod 0.95 m
A 2.0-kg solid cylinder (radius = 0.10 m, length = 0.50 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.75 m high and 5.0 m long. When the cylinder reaches the bottom of the ramp, what are(a) Its total kinetic energy,(b) Its rotational kinetic
A 2.5-kg solid sphere (radius = 0.10 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.75 m high and 5.6 m long. When the sphere reaches the bottom of the ramp, what are(a) Its total kinetic energy,(b) Its rotational kinetic energy,(c) Its
As you switch a fan setting from its slowest speed to its highest, its angular speed v triples.(a) Does the period of rotation T of the fan blade increase, decrease, or stay the same? Explain.(b) What is the ratio of the new rotation period to the old value, Tnew/Told?
When you stand on the observation deck of the Empire State Building in New York, is your linear speed due to the Earth's rotation greater than, less than, or the same as when you were waiting for the elevators on the ground floor?
What linear speed must a 0.065-kg hula hoop have if its total kinetic energy is to be 0.12 J? Assume the hoop rolls on the ground without slipping.
A pilot performing a horizontal turn will lose consciousness if she experiences a centripetal acceleration greater than 7.00 times the acceleration of gravity. What is the minimum radius turn she can make without losing consciousness if her plane is flying with a constant speed of 245 m/s?
The Ruby-throated Hummingbird (Archilochus colubris) can flap its wings with an angular speed of 346 rad/s. What is the period of its flapping motion?
The angular velocity of a rotating wheel as a function of time is shown in the graph in FIGURE 10-36. What is the angular displacement of the wheel, Î¸ - Î¸0, between the times t = 0 and t = 5 s?
A 68-kg commuter rides on an 8.1-kg bicycle. Each bicycle wheel is a hoop of radius 33 cm and mass 1.4 kg.(a) What energy must the biker supply to move at 7.2 m/s? Include the kinetic energy of the biker, the kinetic energy of the bike frame, and the kinetic energy of the rotating wheels.(b) What
Place two quarters on a table with their rims touching, as shown in FIGURE 10-37. While holding one quarter fixed, roll the other one-without slipping-around the circumference of the fixed quarter until it has completed one round trip. How many revolutions has the rolling quarter made about its
The object shown in FIGURE 10-38 can be rotated in three different ways: case 1, rotation about the x axis; case 2, rotation about the y axis; and case 3, rotation about the z axis. Rank these three cases in order of increasing moment of inertia. Indicate ties where appropriate.
A mathematically inclined friend e-mails you the following instructions: "Meet me in the cafeteria the first time after 2:00 p.m. today that the hands of a clock point in the same direction."(a) Is the desired meeting time before, after, or equal to 2:10 p.m.? Explain.(b) Is the desired meeting
Spinning Dragonflies Measurements show that when a dragonfly does a "spin-dry" (Problem 49), it can "spin up" from v0 = 0 to v = 104 rad/s in 0.250 s.(a) Assuming constant angular acceleration, how many revolutions does the dragonfly make in this time?(b) How many revolutions has the dragonfly made
A potter's wheel of radius 6.8 cm rotates with a period of 0.52 s. What are(a) The linear speed(b) The centripetal acceleration of a small lump of clay on the rim of the wheel?(c) How do your answers to parts (a) and (b) change if the period of rotation is doubled?
The record in an old-fashioned record player always rotates at the same angular speed. With CDs, the situation is different. For a CD to play properly, the point on the CD where the laser beam shines must have a linear speed vt = 1.25 m/s, as indicated in FIGURE 10-39.(a) As the CD plays from the
Pigeons are bred to display a number of interesting characteristics. One breed of pigeon, the "roller," is remarkable for the fact that it does a number of backward somersaults as it drops straight down toward the ground. Suppose a roller pigeon drops from rest and free falls downward for a
A bottlenose dolphin (Tursiops truncatus) is about 2.5 m long and has a mass of 250 kg. It can jump 3.5 m above the surface of the water while flipping nose-to-tail at 5.6 rad/s, fast enough to complete 1.5 rotations before landing in the water.(a) How much energy must the dolphin generate to jump
The following table gives the angular speed of a rotating fan blade at various times as it slows to a stop. Find the average angular acceleration for the times(a) t = 0 to t = 2.0 s,(b) t = 0 to t = 4.0 s,(c) t = 2.0 s to t = 4.0 s.Time (s) Angular speed
As a marble with a diameter of 1.6 cm rolls down an incline, its center moves with a linear acceleration of 3.3 m/s2.(a) What is the angular acceleration of the marble?(b) What is the angular speed of the marble after it rolls for 1.5 s from rest?
A rubber ball with a radius of 3.2 cm rolls along the horizontal surface of a table with a constant linear speed v. When the ball rolls off the edge of the table, it falls 0.66 m to the floor below. If the ball completes 0.37 revolution during its fall, what was its linear speed, v?
A yo-yo moves downward until it reaches the end of its string, where it "sleeps." As it sleeps-that is, spins in place-its angular speed decreases from 35 rad/s to 25 rad/s. During this time it completes 120 revolutions.(a) How much time did it take for the yo-yo to slow from 35 rad/s to 25
(a) An automobile with tires of radius 32 cm accelerates from 0 to 45 mph in 9.1 s. Find the angular acceleration of the tires.(b) How does your answer to part (a) change if the radius of the tires is halved?
Yomega ("The yo-yo with a brain") is constructed with a clever clutch mechanism in its axle that allows it to rotate freely and "sleep" when its angular speed is greater than a certain critical value. When the yo-yo's angular speed falls below this value, the clutch engages, causing the yo-yo to
The rotor in a centrifuge has an initial angular speed of 430 rad/s. After 8.2 s of constant angular acceleration, its angular speed has increased to 550 rad/s. During this time, what were(a) The angular acceleration of the rotor(b) The angle through which it turned?
The Sun, with Earth in tow, orbits about the center of the Milky Way galaxy at a speed of 137 miles per second, completing one revolution every 240 million years.(a) Find the angular speed of the Sun relative to the center of the Milky Way.(b) Find the distance from the Sun to the center of the
A person walks into a room and switches on the ceiling fan. The fan accelerates with constant angular acceleration for 15 s until it reaches its operating angular speed of 1.9 rotations/s-after that its speed remains constant as long as the switch is "on." The person stays in the room for a short
When astronauts return from prolonged space flights, they often suffer from bone loss, resulting in brittle bones that may take weeks for their bodies to rebuild. One solution may be to expose astronauts to periods of substantial "g forces" in a centrifuge carried aboard their spaceship. To test
A thin, uniform rod of length L and mass M is pivoted about one end, as shown in FIGURE 10-40. The rod is released from rest in a horizontal position, and allowed to swing downward without friction or air resistance. When the rod is vertical, what are(a) Its angular speed Ï‰(b) The tangential
Four objects, a, b, c, and d, have the initial angular velocities and angular accelerations given in the following table. Determine the angular velocity of each object after an elapsed time of 3.5 s.
In the previous problem, suppose a small metal ball of mass m = 2M is attached to the rod a distance d from the pivot. The rod and ball are released from rest in the horizontal position.(a) Show that when the rod reaches the vertical position, the speed of its tip is(b) At what finite value of d/L
A wooden plank rests on two soup cans laid on their sides. Each can has a diameter of 6.5 cm, and the plank is 3.0 m long. Initially, one can is placed 1.0 m inward from either end of the plank, as FIGURE 10-41 shows. The plank is now pulled 1.0 m to the right, and the cans roll without
A person rides on a 12-m-diameter Ferris wheel that rotates at the constant rate of 8.1 rpm. Calculate the magnitude and direction of the force that the seat exerts on a 65-kg person when he is(a) At the top of the wheel,(b) At the bottom of the wheel,(c) Halfway up the wheel.
A solid sphere with a diameter of 0.17 m is released from rest; it then rolls without slipping down a ramp, dropping through a vertical height of 0.61 m. The ball leaves the bottom of the ramp, which is 1.22 m above the floor, moving horizontally (FIGURE 10-42).(a) Through what horizontal distance
Rank the four curves shown in Figure 10-43 in order of increasing radius. Indicate ties where appropriate.
A particular experimental protocol calls for measuring the physiological parameters during exercise with 2.00g at the feet. What angular speed in rpm must the platform in this test model have in order to produce this centripetal acceleration at the feet?A. 3.20 rpmB. 26.5 rpmC. 30.6 rpmD. 57.8 rpm
If the acceleration is 2.00g at the feet, what is the acceleration at the heart?A. 0B. 0.560gC. 1.40gD. 2.00g
Which of the curves shown in Figure 10-43 corresponds to the location of the feet in this test model?A. 1B. 2C. 3D. 4
Suppose we race a disk and a hollow spherical shell, like a basketball. The spherical shell has a mass M and a radius R; the disk has a mass 2M and a radius 2R.(a) Which object wins the race? If the two objects are released at rest, and the height of the ramp is h = 0.75 m, find the speed of(b) The
Consider a race between the following three objects: object 1, a disk; object 2, a solid sphere; and object 3, a hollow spherical shell. All objects have the same mass and radius.(a) Rank the three objects in the order in which they finish the race. Indicate a tie where appropriate.(b) Rank the
What purpose does the tail rotor on a helicopter serve?
Suppose a diver springs into the air with no initial angular velocity. Can the diver begin to rotate by folding into a tucked position? Explain.
A car pitches down in front when the brakes are applied sharply. Explain this observation in terms of torques.
When a motorcycle accelerates rapidly from a stop it sometimes "pops a wheelie"; that is, its front wheel may lift off the ground. Explain this behavior in terms of torques.
Give an example of a system in which the net force is zero but the net torque is nonzero.
Give two everyday examples of objects that are not in static equilibrium.
To tighten a spark plug, it is recommended that a torque of 15 N ∙ m be applied. If a mechanic tightens the spark plug with a wrench that is 25 cm long, what is the minimum force necessary to create the desired torque?
A torque of 0.97 N ∙ m is applied to a bicycle wheel of radius 35 cm and mass 0.75 kg. Treating the wheel as a hoop, find its angular acceleration.
When a ceiling fan rotating with an angular speed of 3.66 rad/s is turned off, a frictional torque of 0.125 N # m slows it to a stop in 31.8 s. What is the moment of inertia of the fan?
When the play button is pressed, a CD accelerates uniformly from rest to 450 rev/min in 3.0 revolutions. If the CD has a radius of 6.0 cm and a mass of 17 g, what is the torque exerted on it?
A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.66 m and mass 10.9 kg, find the torque the person must exert on the ladder to give it an angular acceleration of 0.333 rad/s2.
A 0.180-kg wooden rod is 1.25 m long and pivots at one end. It is held horizontally and then released.(a) What is the angular acceleration of the rod after it is released?(b) What is the linear acceleration of a spot on the rod that is 0.95 m from the axis of rotation?(c) At what location along the
A wheel on a game show is given an initial angular speed of 1.22 rad/s. It comes to rest after rotating through 0.75 of a turn.(a) Find the average torque exerted on the wheel given that it is a disk of radius 0.71 m and mass 6.4 kg.(b) If the mass of the wheel is doubled and its radius is halved,

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