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physics
mechanics
Questions and Answers of
Mechanics
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 ω = 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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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, θ - θ0, 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
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
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
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
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
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
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
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
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
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 =
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
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.
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
(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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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