A diver tucks her body in midnight, decreasing her moment

Problem 1CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Two forces produce the same torque. Does it follow that they have the same magnitude? Explain.

Problem 124IP Suppose everything in the system is as described in Active Example 11-5 except that the child approaches the merry-go-round in a direction that is not tangential Find the angle ? between the direction of motion and the outward radial direction (as in Example 11-8) that is required if the final angular speed of the system is to be 0.272 rad/s.

Problem 1P 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?

Problem 3P A 1.61-kg bowling trophy is held at arm's length, a distance of 0.605 m from the shoulder joint. What torque does the trophy exert about the shoulder if the arm is (a) horizontal, or (b) at an angle of 22.5° below the horizontal?

Problem 2CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. A car pitches down in front when the brakes are applied sharply. Explain this observation in terms of torques.

The gardening tool shown in Figure 11–21 is used to pull weeds. If a 1.23-N.m torque is required to pull a given weed, what force did the weed exert on the tool?

Problem 3CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. A tightrope walker uses a long pole to aid in balancing. Why?

A person slowly lowers a 3.6-kg crab trap over the side of a dock, as shown in Figure 11–22. What torque does the trap exert about the person’s shoulder?

Problem 6CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Give an example of a system in which the net force is zero but the net torqueis nonzero.

Problem 4CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. 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.

Problem 7CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Is the normal force exerted by the ground the same for all four tires on your car? Explain.

Problem 5CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Give an example of a system in which the net torque is zero but the net force is nonzero.

Consider the pulley–block systems shown in Conceptual Checkpoint 11–1. (a) Is the tension in the string on the left-hand rotating system greater than, less than, or equal to the weight of the mass attached to that string? (b) Choose the best explanation from among the following: I.The mass is in free fall once it is released. II. The string rotates the pulley in addition to supporting the mass. III. The mass accelerates downward.

Problem 8P Consider the pulley-block systems shown in Conceptual Checkpoint 11–1. (a) Is the tension in the string on the left-hand rotating system greater than, less than, or equal to the tension in the string on the right-hand rotating system? (b) Choose the best explanation from among the following: I. The mass in the right-hand system has the greater downward acceleration. II. The masses are equal. III. The mass in the left-hand system has the greater downward acceleration.

A person holds a 1.42-N baseball in his hand, a distance of 34.0 cm from the elbow joint, as shown in Figure 11–23. The biceps, attached at a distance of 2.75 cm from the elbow, exerts an upward force of 12.6 N on the forearm. Consider the forearm and hand to be a uniform rod with a mass of 1.20 kg. (a) Calculate the net torque acting on the forearm and hand. Use the elbow joint as the axis of rotation. (b) If the net torque obtained in part (a) is nonzero, in which direction will the forearm and hand rotate? (c) Would the torque exerted on the forearm by the biceps increase or decrease if the biceps were attached farther from the elbow joint?

Problem 8CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Give two everyday examples of objects that are not in static equilibrium.

Problem 9CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Give two everyday examples of objects that are in static equilibrium.

Problem 11P When a ceiling fan rotating with an angular speed of 2.75 rad/s is turned off, a frictional torque of 0.120 N · m slows it to a stop in 22.5 s. What is the moment of inertia of the fan?

Problem 10P 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.

Problem 12CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. What purpose does the tail rotor on a helicopter serve?

Problem 10CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Can an object have zero translational acceleration and, at the same time, have nonzero angular acceleration? if your answer is no, explain why not. If your answer is yes, give a specific example.

Problem 11CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Stars form when a large rotating cloud of gas collapses. What happens to the angular speed of the gas cloud as it collapses?

Problem 9P Suppose a torque rotates your body about one of three different axes of rotation: case A, an axis through your spine; case B, an axis through yorrr hips; and case C, an axis through your ankles. Rank these three axes of rotation in increasing order of the angular acceleration produced by the torque. Indicate ties where appropriate.

Problem 12P 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?

Problem 13P A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.15 m and mass 8.42 kg, find the torque the person must exert on the ladder to give it an angular acceleration of 0.302 rad/s2.

Problem 13CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Is it possible to change the angular momentum of an object without changing its linear momentum? If your answer is no, explain why not. If your answer is yes, give a specific example.

Problem 14P A wheel on a gameshow is given aninitiai 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, will the angle through which it rotates before coming to rest increase, decrease, or stay the same? Explain. (Assume that the average torque exerted on the wheel is unchanged.)

Problem 17P A motorcycle accelerates from rest, and both the front and rear- tires roll without slipping. (a) Is the force exerted by the ground on the rear tire in the forward or in the backward direction? Explain. (b) Is the force exerted by the ground on the front tire in the forward or in the backward direction? Explain. (c) If the moment of inertia of the front tire is increased, will the motorcycle's acceleration increase, decrease, or stay the same? Explain.

Problem 14CQ Answers to odd-numbered Conceptual Questions can be found in the back of the book. Suppose a diver springs into the air with no initial angular velocity. Can the diver begin to rotate by folding into atucked position? Explain.

Problem 16P The L-shaped object described in Problem 15 can be rotated in one of the following three ways: case A, about the x axis; case B, about the y axis; and case C, about the z axis (which passes through the origin perpendicular' to the plane of the figure). If the same torque r is applied in the of these cases, rank them in increasing order of the resulting angular acceleration. Indicate ties where appropriate.

The L-shaped object in Figure 11–24 consists of three masses connected by light rods. What torque must be applied to this object to give it an angular acceleration of \(1.20\ \mathrm{ rad/s^2}\) if it is rotated about (a) the x axis, (b) the y axis, or (c) the z axis (which is through the origin and perpendicular to the page)? ________________ Equation Transcription: Text Transcription: 1.20 rad/s^2

Problem 20P Repeat the previous problem, only now assume the reel has a friction clutch that exerts a restraining torque of 0.047 N · m.

Problem 19P A fish takes the bait and pulls on the line with a force of 2.2 N. The fishing reel, which rotates without friction, is a cylinder of radius 0.055 m and mass 0.99 kg. (a) What is the angular acceleration of the fishing reel? (b) How much line does the fish pull from the reel in 0.25 s?

A torque of 13N.m is applied to the rectangular object shown in Figure 11–25. The torque can act about the x axis, the y axis, or the z axis, which passes through the origin and points out of the page. (a) In which case does the object experience the greatest angular acceleration? The least angular acceleration? Explain. Find the angular acceleration when the torque acts about (b) the x axis, (c) the y axis, and (d) the z axis.

Problem 21P Suppose the person in Active Example 11-3 climbs higher on the ladder. (a) As a result, is the ladder more likely, less likely, or equally likely to slip? (b) Choose the best explanation from among the following: I. The forces are the same regardless of the person's position. II. The magnitude of f 2 must increase as the person moves upward. III. When the person is higher, the ladder presses down harder on the floor.

Problem 23P To loosen the lid on a jar of jam 8.9 cm in diameter, a torque of 8.5 N · m must be applied to the circumference of the lid. If a jar wrench whose handle extends 15 cm from the center of the jar is attached to the lid, what is the minimum force required to open the jar?

Problem 22P A string that passes over a pulley has a 0.321-kg mass attached to one end and a 0.635-kg mass attached to the other end. The pulley, which is a disk of radius 9.40 cm, has friction in its axle. What is the magnitude of the frictional torque that must be exerted by the axle if the system is to be in static equilibrium?

Problem 24P Consider the system in Active Example 11-1, this time with the axis of rotation at the location of the child. Write out both the condition for zero net force and the condition for zero net torque. Solve for the two forces.

Problem 25P Referring to the person holding a baseball in Problem 5, suppose the biceps exert just enough upward force to keep the system in static equilibrium. (a) Is the force exerted by the biceps more than, less than, or equal to the combined weight of the forearm, hand, and baseball? Explain. (b) Determine the force exerted by the biceps.

To determine the location of her center of mass, a physics student lies on a lightweight plank supported by two scales 2.50 m apart, as indicated in Figure 11–26. If the left scale reads 290 N, and the right scale reads 122 N, find (a) the student’s mass and (b) the distance from the student’s head to her center of mass.

A 0.122-kg remote control 23.0 cm long rests on a table, as shown in Figure 11–28, with a length L overhanging its edge. To operate the power button on this remote requires a force of 0.365 N. How far can the remote control extend beyond the edge of the table and still not tip over when you press the power button? Assume the mass of the remote is distributed uniformly, and that the power button is 1.41 cm from the overhanging end of the remote.

A set of fossilized triceratops footprints discovered in Texas show that the front and rear feet were 3.2 m apart, as shown in Figure 11–27. The rear footprints were observed to be twice as deep as the front footprints. Assuming that the rear feet pressed down on the ground with twice the force exerted by the front feet, find the horizontal distance from the rear feet to the triceratops’s center of mass.

Problem 28P A schoolyard teeter-totter with a total length of 5.2 m and a mass of 38 kg is pivoted at its center. A 19-kg child sits on one end of the teeter-totter. (a) Where should a parent push vertically downward with a force of 210 N in order to hold the teeter-totter level? (b) Where should the parent push with a force of 310 N? (c) How would your answers to parts (a) and (b) change if the mass of the teeter-totter were doubled? Explain.

Problem 30P A 0.16-kg meter stick is held perpendicular to a vertical wall by a 2.5-m string going from the wall to the far end of the stick. (a) Find the tension in the string. (b) If a shorter string is used, will its tension be greater than, less than, or the same as that found in part (a)? (c) Find the tension in a 2.0-m string.

Problem 32P Babe Ruth steps to the plate and casually points to left center field to indicate the location of his next home run. The mighty Babe holds his bat across his shoulder, with one hand holding the small end of the bat. The bat is horizontal, and the distance from the small end of the bat to the shoulder is 22.5 cm. If the bat has a mass of 1.10 kg and has a center of mass that is 67.0 cm from the small end of the bat, find the magnitude and direction of the force exerted by (a) the hand and (b) the shoulder.

Repeat Example 11–4, this time with a uniform diving board that weighs 225 N.

Repeat Active Example 11–3, this time with a uniform 7.2-kg ladder that is 4.0 m long.

Problem 34P In the previous problem, suppose the wire is shortened, so that the rod now makes an angle of 35° with the horizontal. The wire is horizontal, as before. (a) Do you expect the tension in the wire to increase, decrease, or stay the same as a result of its new length? Explain. (b) Calculate the tension in the wire. Reference Problem: • • A uniform metal rod, with a mass of 3.7 kg and a length of 1.2 m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.51 m above the base of the rod holds the rod at an angle of 25° above the horizontal. The wire is attached to the top of the rod. (a) Find the tension in the wire. Find (b) the horizontal and (c) the vertical components of the force exerted on the rod by the hinge.

Problem 33P A uniform metal rod, with a mass of 3.7 kg and a length of 1.2 m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.51 m above the base of the rod holds the rod at an angle of 25° above the horizontal. The wire is attached to the top of the rod. (a) Find the tension in the wire. Find (b) the horizontal and (c) the vertical components of the force exerted on the rod by the hinge.

A rigid, vertical rod of negligible mass is connected to the floor by a bolt through its lower end, as shown in Figure 11–29. The rod also has a wire connected between its top end and the floor. If a horizontal force F is applied at the midpoint of the rod, find (a) the tension in the wire, and (b) the horizontal and (c) the vertical components of force exerted by the bolt on the rod. ________________ Equation Transcription: Text Transcription: 45^o

Astick with a mass of 0.214 kg and a length of 0.436 m rests in contact with a bowling ball and a rough floor, as shown in Figure 11–31. The bowling ball has a diameter of 21.6 cm, and the angle the stick makes with the horizontal is \(30.0^\circ\). You may assume there is no friction between the stick and the bowling ball, though friction with the floor must be taken into account. (a) Find the magnitude of the force exerted on the stick by the bowling ball. (b) Find the horizontal component of the force exerted on the stick by the floor. (c) Repeat part (b) for the vertical component of the force. ________________ Equation Transcription: Text Transcription: 30^o 30^o

Problem 39P A uniform crate with a mass of 16.2 kg rests on a floor with a coefficient of static friction equal to 0.571. The crate is a uniform cube with sides 1.21 m in length. (a) What horizontal force applied to the top of the crate will initiate tipping? (b) If the horizontal force is applied halfway to the top of the crate, it will begin to slip before it tips. Explain.

shows the forces acting on a sprinter’s foot just before she takes off at the start of the race. Find the magnitude of the force exerted on the heel by the Achilles tendon, \(F_ \mathrm H\), and the magnitude of the force exerted on the foot at the ankle joint, \(F_ \mathrm J\). ________________ Equation Transcription: Text Transcription: F_H F_J F_H F_J 59.2^o N=223 N

Problem 40P In the previous problem, (a) what is the minimum height where the force F can be applied so that the crate begins to tip before sliding? (b) What is the magnitude of the force in this case? Reference Problem: • • • IP A uniform crate with a mass of 16.2 kg rests on a floor with a coefficient of static friction equal to 0.571. The crate is a uniform cube with sides 1.21 m in length, (a) What horizontal force applied to the top of the crate will initiate tipping? (b) If the horizontal force is applied halfway to the top of the crate, it will begin to slip before it lips. Explain.

Problem 41P A hand-held shopping basket 62.0 cm long has a 1.81-kg carton of milk at one end, and a 0.722-kg box of cereal at the other end. Where should a 1.80-kg container of orange juice be placed so that the basket balances at its center?

If the cat in Active Example 11–2 has a mass of 2.8 kg, how close to the right end of the two-by-four can it walk before the board begins to tip?

Three identical, uniform books of length L are stacked one on top the other. Find the maximum overhang distance d in Figure 11–32 such that the books do not fall over.

Problem 47P In the previous problem, (a) is the tension in the rope greater than, less than, or equal to the weight of the bucket? Explain. (b) Calculate the tension in the rope.

Problem 43P A 0.34-kg meterstick balances at its center. If a necklace is suspended from one end of the stick, the balance point moves 9.5 cm toward that end. (a) Is the mass of the necklace more than, less than, or the same as that of the meterstick? Explain. (b) Find the mass of the necklace.

A \(2.85-\mathrm{kg}\) bucket is attached to a disk-shaped pulley of radius \(0.121 \mathrm{~m}\) and mass \(0.742 \mathrm{~kg}\). If the bucket is allowed to fall, (a) what is its linear acceleration? (b) What is the angular acceleration of the pulley? (c) How far does the bucket drop in \(1.50 \mathrm{~s}\) ?

Problem 48P A child exerts a tangential 42.2-N force on the rim of a disk-shaped merry-go-round with a radius of 2.40 m. If the merry-go-round starts at rest and acquires an angular speed of 0.0860 rev/s in 3.50 s, what is its mass?

Problem 49P You pull downward with a force of 28 N on a rope that passes over a disk-shaped pulley of mass 1.2 kg and radius 0.075 m. The other end of the rope is attached to a 0.67-kg mass. (a) Is the tension in the rope the same on both sides of the pulley? If not, which side has the largest tension? (b) Find the tension in the rope on both sides of the pulley.

Problem 50P Referring to the previous problem, find the linear acceleration of the 0.67-kg mass.

Problem 52P Atwood's Machine An Atwood's machine consists of two masses, m\ and m-i, connected by a string that passes over a pulley. If the pulley is a disk of radius R and mass M, find the acceleration of the masses.

Problem 53P Calculate the angular momentum of the Earth about its own axis, due to its daily rotation. Assume that the Earth is a uniform sphere.

Repeat the previous problem for the case of jogger 2, whose speed is 2.68 m/s and whose mass is 58.2 kg.

Problem 54P A 0.015-kg record with a radius of!5 cm rotates with an angular speed of rpm. Find the angular momentum of the record.

Jogger 1 in Figure 11–33 has a mass of 65.3 kg and runs in a straight line with a speed of 3.35 m/s. (a) What is the magnitude of the jogger’s linear momentum? (b) What is the magnitude of the jogger’s angular momentum with respect to the origin, O?

Problem 55P Tn the previous problem, a 1.1-g fly lands on the rim of the record. What is the fly's angular momentum?

Problem 59P A torque of 0.12 N m is applied to an egg beater. (a) Tf the egg beater starts at rest, what is its angular momentum after 0.65 s? (b) Tf the moment of inertia of the egg beater is 2.5 × 10?3 kg · m2, what is its angular speed after 0.65 s?

Problem 60P0. A windmill has an initial angular momentum of 8500 kg · m2 /s. The wind picks up, and 5.86 s later the windmill's angular momentum is 9700 kg · m2 /s. What was the torque acting on the windmill, assuming it was constant during this time?

Suppose jogger 3 in Figure 11–33 has a mass of 62.2 kg and a speed of 5.85 m/s. (a) Is the magnitude of the jogger’s angular momentum greater with respect to point A or point B? Explain. (b) Is the magnitude of the jogger’s angular momentum with respect to point B greater than, less than, or the same as it is with respect to the origin, O? Explain. (c) Calculate the magnitude of the jogger’s angular momentum with respect to points A, B, and O.

Problem 61P Two gerbils run in place with a linear speed of 0.55 m/s on an exercise wheel that is shaped like a hoop. Find the angular momentum of the system if the gerbil has a mass of 0.22 kg and the exercise wheel has a radius of 9.5 cm and a mass of 5.0 g.

Apuck on a horizontal, frictionless surface is attached to a string that wraps around a pole of finite radius, as shown in Figure 11–35. (a) As the puck moves along the spiral path, does its speed increase, decrease, or stay the same? Explain. (b) Does its angular momentum increase, decrease, or stay the same? Explain.

Problem 62P A student rotates on a frictionless piano stool with his arms outstretched, a heavyweight in the hand. Suddenly he lets go of the weights, and they fall to the floor. As a result, does the student's angular speed increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The loss of angular momentum when the weights are dropped causes the student to rotate more slowly. II. The student's moment of inertia is decreased by dropping the weights. III. Dropping the weights exerts no torque on the student, but the floor exerts a torque on the weights when they land.

Problem 65P As an ice skater begins a spin, his angular speed is 3.17 rad/s. After pulling in Ms arms, his angular speed increases to 5.46 rad/s. Find the ratio of the skater's final moment of inertia to his initial moment of inertia.

Calculate both the initial and the final kinetic energies of the system described in Active Example 11–5.

Problem 67P A diver tucks her body in midnight, decreasing her moment of inertia by a factor of two. By what factor does her angular speed change?

Problem 68P In the previous problem, (a) does the diver's kinetic energy increase, decrease, or stay the same? (b) Calculate the ratio of the final kinetic energy to the initial kinetic energy for the diver.

Apuck on a horizontal, frictionless surface is attached to a string that passes through a hole in the surface, as shown in Figure 11–34. As the puck rotates about the hole, the string is pulled downward, bringing the puck closer to the hole. During this process, do the puck’s (a) linear speed, (b) angular speed, and (c) angular momentum increase, decrease, or stay the same?

Problem 70P In the previous problem, (a) does the kinetic energy of the system increase, decrease, or stay the same when the person jumps on the merry-go-round? (b) Calculate the initial and final kinetic energies for this system. Reference Problem: . •• A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of 0.641 rev/s. A 59.4-kg person running tangential to the rim of the merry-go-round at 3.41 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. What is the final angular speed of the merry-go-round?

Problem 72P Referring to the previous problem, (a) does the kinetic energy of the mass-student-stool system increase, decrease, or stay the same as the mass is caught? (b) Calculate the initial and final kinetic energies of the system. REFERENCE PROBLEM: A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.1 kgm2. A second student tosses a 1.5-kg mass with a speed of 2.7 m/s to the student on the stool, who catches it at a distance of 0.40 m from the axis of rotation. What is the resulting angular speed of the student and the stool?

Problem 69P A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of 0, 641 rev/s. A 59.4-kg person running tangential to the rim of the merry-go-round at 3.41 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. What is the final angidar speed of the merry-go-round?

Problem 75P A child of mass m stands at rest near the rim of a stationary merry-go-round of radius R and moment of inertia I. The child now begins to walk around the circumference of the merry-go-round with a tangential speed v with respect to the merry-go-round's surface. (a) What is the child's speed with respect to the ground? Check your results in the limits (b) I ? 0 and (c) I ??

Problem 76P Two spheres of equal mass and radius are rolling across the floor with the same speed. Sphere 1 is a uniform solid; sphere 2 is hollow. Is the work required to stop sphere 1 greater than, less than, or equal to the work required to stop sphere 2? (b) Choose the best explanation from among the following: I. Sphere 2 has the greater moment of inertia and hence the greater rotational kinetic energy. II. The spheres have equal mass and speed; therefore, they have the same kinetic energy. III. The hollow sphere has less kinetic energy.

Problem 77P How much work must be done to accelerate a baton from rest to an angular speed of 7.4 rad/s about its center? Consider the baton to be a uniform rod of length 0.53 m and mass 0.44 kg.

Problem 79P A person exerts a tangential force of 36.1 N on the rim of a disk-shaped merry-go-round of radius 2.74 m and mass 167 kg. If the merry-go-round starts at rest, what is its angular speed after the person has rotated it through an angle of 32.5°?

Problem 71P A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.1 kg · m2. A second student tosses a 1.5-kg mass with a speed of 2.7 m/s to the student on the stool, who catches it at a distance of 0.40 m from the axis of rotation. What is the resulting angular speed of the student and the stool?

Problem 74P A student on a piano stool rotates freely with an angular speed of 2.95 rev/s. The student holds a 1.25-kg mass in the outstretched arm, 0.759 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.43 kg -m2, a value that remains constant. (a) As the student pulls his arms inward, his angular speed increases to 3.54 rcv/s. How far are the masses from the axis of rotation at this time, considering the masses to be points? (b) Calculate the initial and final kinetic energies of the system.

Problem 81P A popular make of dental drill can operate at a speed of 42, 500 rpm while producing a torque of 3.68 oz · in. What is the power output of this drill? Give your answer in watts.

Problem 84P A circular saw blade accelerates from rest to an angular speed of 3620 rpm in 6.30 revolutions. (a) Find the torque exerted on the saw blade, assuming it is a disk of radius 15.2 cm and mass 0.755 kg. (b) Is the angular speed of the saw blade after 3.15 revolutions greater than, less than, or equal to 1810 rpm? Explain. (c) Find the angular speed of the blade after 3.15 revolutions.

A uniform disk stands upright on its edge, and rests on a sheet of paper placed on a tabletop. If the paper is pulled horizontally to the right, as in Figure 11–36, (a) does the disk rotate clockwise or counterclockwise about its center? Explain. (b) Does the center of the disk move to the right, move to the left, or stay in the same location? Explain.

Problem 78P Turning a doorknob through. 0.25 of a revolution requires 0.14 J of work. What is the torque required to turn the doorknob?

A disk and a hoop (bicycle wheel) of equal radius and mass each have a string wrapped around their circumferences. Hanging from the strings, halfway between the disk and the hoop, is a block of mass m, as shown in Figure 11–38. The disk and the hoop are free to rotate about their centers. When the block is allowed to fall, does it stay on the center line, move toward the right, or move toward the left? (b) Choose the best explanation from among the following: I. The disk is harder to rotate, and hence its angular acceleration is less than that of the wheel. II. The wheel has the greater moment of inertia and unwinds more slowly than the disk. III. The system is symmetric, with equal mass and radius on either side.

Consider the two rotating systems shown in Figure 11–37, each consisting of a mass m attached to a rod of negligible mass pivoted at one end. On the left, the mass is attached at the midpoint of the rod; to the right, it is attached to the free end of the rod. The rods are released from rest in the horizontal position at the same time. When the rod to the left reaches the vertical position, is the rod to the right not yet vertical (location A), vertical (location B), or past vertical (location C)? Explain.

The L-shaped object in Figure 11–24 consists of three masses connected by light rods. Find the work that must be done on this object to accelerate it from rest to an angular speed of 2.35 rad/s about (a) the x axis, (b) the y axis, and (c) the z axis (which is through the origin and perpendicular to the page).

The rectangular object in Figure 11–25 consists of four masses connected by light rods. What power must be applied to this object to accelerate it from rest to an angular speed of 2.5 rad/s in 6.4 s about (a) the x axis, (b) the y axis, and (c) the z axis (which is through the origin and perpendicular to the page)?

Problem 90GP Suppose the Earth were to magically expand, doubling its radius while keeping its mass the same. Would the length of the day increase, decrease, or stay the same? Explain.

Problem 88GP A beetle sits at the rim of a turntable that is at rest but is free to rotate about a vertical axis. Suppose the beetle now begins to walk around the perimeter of the turntable. Does the beetle move forward, backward, or does it remain in the same location relative to the ground? Answer for two different cases, (a) the turntable is much more massive than the beetle and (b) the turntable is massless.

Problem 73P A turntable with a moment of inertia of 5.4 × 10 ?3 kgm2 rotates freely with an angular speed 33 of rpm. Riding on the rim of the turntable, 15 cm from the center, is a cute, 32-g mouse. (a) if the mouse walks to the center of the turntable, will the turntable rotate faster, slower, or at the same rate? Explain. (b) Calculate the angular speed of the turntable when the mouse reaches the center.

Problem 91GP After getting a drink of water, a hamster jumps onto an exercise wheel for a run. A few seconds later the hamster is running in place with a speed of 1, 3 m/s. Find the work done by the hamster to get the exercise wheel moving, assuming it is a hoop of radius 0.13 m and mass 6.5 g.

Problem 89GP A beetle sits near the rim of a turntable that is rotating without friction about a vertical axis. The beetle now begins to walk toward the center of the turntable. As a result, does the angular speed of the turntable increase, decrease, or stay the same? Explain.

Problem 92GP A 47.0-kg uniform rod 4.25 m long is attached to a wall with a hinge at one end. The rod is held in a horizontal position by, a wire attached to its other end. The wire makes an angle of 30.0° with the horizontal, and is bolted to the wall directly above the hinge. If the wire can withstand a maximum tension of 1450 N before breaking, how far from the wall can a 68.0-kg person sit without breaking the wire?

Problem 98GP You hold a uniform, 28-g pen horizontal with your thumb pushing down on one end and your index finger pushing upward 3.5 cm from, your thumb. The pen is 14 cm long. (a) Which of these two forces is greater in magnitude? (b) Find the two forces.

A puck attached to a string moves in a circular path on a frictionless surface, as shown in Figure 11–34. Initially, the speed of the puck is v and the radius of the circle is r. If the string passes through a hole in the surface, and is pulled downward until the radius of the circular path is r/2, (a) does the speed of the puck increase, decrease, or stay the same? (b) Calculate the final speed of the puck.

Paleontologists believe that Tyrannosaurus rex stood and walked with its spine almost horizontal, as indicated in Figure 11–41, and that its tail was held off the ground to balance its upper torso about the hip joint. Given that the total mass of T. rex was 5400 kg, and that the placement of the center of mass of the tail and the upper torso was as shown in Figure 11–41, find the mass of the tail required for balance.

When you arrive at Duke’s Dude Ranch, you are greeted by the large wooden sign shown in Figure 11–42. The left end of the sign is held in place by a bolt, the right end is tied to a rope that makes an angle of \(20^\circ\) with the horizontal. If the sign is uniform, 3.20 m long, and has a mass of 16.0 kg, what are (a) the tension in the rope, and (b) the horizontal and vertical components of the force, F, exerted by the bolt? ________________ Equation Transcription: Text Transcription: 20.0^o vec{F} vec{F} 20.0^o m vec{g} vec{T} L=1.60 m L=1.60 m

The masseter muscle, the principal muscle for chewing, is one of the strongest muscles for its size in the human body. It originates on the lower edge of the zygomatic arch (cheekbone) and inserts in the angle of the mandible. Referring to the lower diagram in Figure 11–39, where \(d=7.60\ \mathrm {cm}\) and \(D=10.85\ \mathrm {cm}\), (a) find the torque produced about the axis of rotation by the masseter muscle. The force exerted by the masseter muscle is \(F_\mathrm M=455\ \mathrm {N}\). (b) Find the biting force, \(F_\mathrm {B}\), exerted on the mandible by the upper teeth. Find (c) the horizontal and (d) the vertical component of the force \(F_\mathrm {J}\) exerted on the mandible at the joint where it attaches to the skull. Assume that the mandible is in static equilibrium, and that upward is the positive vertical direction. Equation Transcription: Text Transcription: d=7.60 cm D=10.85 cm F_M=455 N FB F_J F_B F_M 26.0^o F_J

Problem 99GP In Active Example 11-3, suppose the ladder is uniform, 4.0 m long, and weighs 60.0 N. Find the forces exerted on the ladder when the person is (a) halfway up the ladder and (b) three-fourths of the way up the ladder.

You are designing exercise equipment to operate as shown in Figure 11–40, where a person pulls upward on an elastic cord. The cord behaves like an ideal spring and has an unstretched length of 31 cm. If you would like the torque about the elbow joint to be \(81\ \mathrm {N\cdot m}\) in the position shown, what force constant, k, is required for the cord? ________________ Equation Transcription: Text Transcription: 81 N{cdot}m 39^o 61^o

A woman might wear a pair of flat shoes to work during the day, as in Figure 11–43 (a), but a pair of high heels, Figure 11–43 (b), when going out for the evening. Assume that each foot supports half her weight, \(w=W/2=279\ \mathrm N\), and that the forces exerted by the floor on her feet occur at the points A and B in both figures. Find the forces \(F_\mathrm A\) (point A) and \(F_\mathrm B\) (point B) for (a) flat shoes and (b) high heels. (c) How have the high heels changed the weight distribution between the woman’s heels and toes? ________________ Equation Transcription: Text Transcription: w=W/2=279 N F_A F_B

In Example 11–4, find \(\mathrm {\vec F_1}\) and \(\mathrm {\vec F_2}\) as a function of the distance, x, of the swimmer from the left end of the diving board. Assume that the diving board is uniform and has a mass of 85.0 kg. ________________ Equation Transcription: Text Transcription: vec{F}_1 vec{F}_2

Problem 101GP A 67, 0-kg person stands on a lightweight diving board supported by two pillars, one at the end of the board, the other 1.10 m away. The pillar at the end of the board exerts a downward force of 828 N. (a) How far from that pillar is the person standing? (b) Find the force exerted by the second pillar.

A young girl sits at the edge of a dock by the bay, dipping her feet in the water. At the instant shown in Figure 11–44, she holds her lower leg stationary with her quadriceps muscle at an angle of \(39^\circ\) with respect to the horizontal. Use the information given in the figure, plus the fact that her lower leg has a mass of 3.4 kg, to determine the magnitude of the force, \(F_\mathrm Q\), exerted on the lower leg by the quadriceps. ________________ Equation Transcription: Text Transcription: 39^o F_Q F_Q 29^o 39^o

A crossing guard holds a STOP sign at arm’s length, as shown in Figure 11–45. Her arm is horizontal, and we assume that the deltoid muscle is the only muscle supporting her arm. The weight of her upper arm is \(W_\mathrm {u}=18\ \mathrm N\), the weight of her lower arm is \(W_\mathrm {l}=11\ \mathrm N\), the weight of her hand is \(W_\mathrm {h}=4.0\ \mathrm N\), and the weight of the sign is \(W_\mathrm {s}=8.9\ \mathrm N\). The location where each of these forces acts on the arm is indicated in the figure. A force of magnitude \(f_\mathrm d\) is exerted on the humerus by the deltoid, and the shoulder joint exerts a force on the humerus with horizontal and vertical components given by \(f_\mathrm x\), and \(f_\mathrm y\), respectively. (a) Is the magnitude of \(f_\mathrm d\) greater than, less than, or equal to the magnitude of \(f_\mathrm x\)? Explain. Find (b) \(f_\mathrm d\), (c) \(f_\mathrm x\), and (d) \(f_\mathrm y\). (The weights in Figure 11–45 are drawn to scale; the unknown forces are to be determined. If a force is found to be negative, its direction is opposite to that shown.) Equation Transcription: Text Transcription: W_u=18 N W_1=11 N W_h=4.0 N W_s=8.9 N f_d f_x f_y f_x f_d f_x f_y f_x f_d f_y 18^o W_u W_1 W_h W_s

Problem 107GP Suppose a fourth book, the same as the other three, is added to the stack of books shown in Figure 11-32. (a) What is the maximum overhang distance, d, in this case? (b) If the mass of the book is increased by the same amount, does your answer to part (a) increase, decrease, or stay the same? Explain.

Problem 108GP Suppose partial melting of the polar ice caps increases the moment of inertia of the Earth from 0.331 M E R E 2 to 0.332 M E R E 2. (a) Would the length of a day (the time required for the Earth to complete one revolution about its axis) increase or decrease? Explain. (b) Calculate the change in the length of a day. Give your answer in seconds.

To determine the force a person’s triceps muscle can exert, a doctor uses the procedure shown in Figure 11–46, where the patient pushes down with the palm of his hand on a force meter. Given that the weight of the lower arm is \(Mg=15.6\ \mathrm N\), and that the force meter reads \(F=89.0\ \mathrm N\), what is the force \(F_\mathrm{T}\) exerted vertically upward by the triceps? ________________ Equation Transcription: Text Transcription: Mg=15.6 N F=89.0 N F_T

A bicycle wheel of radius R and mass M is at rest against a step of height 3R/4, as illustrated in Figure 11–47. Find the minimum horizontal force F that must be applied to the axle to make the wheel start to rise up over the step.

A 0.101-kg yo-yo has an outer radius R that is 5.60 times greater than the radius r of its axle. The yo-yo is in equilibrium if a mass m is suspended from its outer edge, as shown in Figure 11–48. Find the tension in the two strings, \(T_1\) and \(T_2\), and the mass m. ________________ Equation Transcription: Text Transcription: T1 T2 T1 T2

Problem 111GP In Problem, assume that the rod has a mass of M and that its bottom end simply rests on the floor, held in place by static friction. If the coefficient of static friction is ?s, find the maximum force F that can be applied to the rod at its midpoint before it slips.

In the previous problem, suppose the rod has a mass of 2.3 kg and the coefficient of static friction is 1/7. (a) Find the greatest force F that can be applied at the midpoint of the rod without causing it to slip. (b) Show that if F is applied 1/8 of the way down from the top of the rod, it will never slip at all, no matter how large the force F.

Problem 113GP A cylinder of mass m and radius r has a string wrapped around its circumference. The upper end of the string is held fixed, and the cylinder is allowed to fall. Show that its linear acceleration is (2/3)g.

Problem 114GP Repeat the previous problem, replacing the cylinder with a solid sphere. Show that its linear acceleration is (5/7)g.

Consider a system of four uniform bricks of length L stacked as shown in Figure 11–49. What is the maximum distance, x, that the middle bricks can be displaced outward before they begin to tip?

Find the values of \(F_{1y}\) and \(F_{2y}\) required to give zero net torque. A. \(F_{1y}=-1.2\ \mathrm N, F_{2y}=3.0\ \mathrm N\) B. \(F_{1y}=1.1\ \mathrm N, F_{2y}=0.75\ \mathrm N\) C. \(F_{1y}=-0.73\ \mathrm N, F_2y=2.5\ \mathrm N\) D. \(F_1y=0.52\ \mathrm N, F_2y=1.3\ \mathrm N\) ________________ Equation Transcription: Text Transcription: F_1y F_2y F_1y=-1.2 N, F_2y=3.0 N F_1y=1.1 N, F_2y=0.75 N F_1y=-0.73 N, F_2y=2.5 N F_1y=0.52 N, F_2y=1.3 N

Find the values of \(F_{1y}\) and \(F_{2y}\) required to give a net torque of \(0.009 \mathrm {N\cdot m}\). This is a torque that would be effective at rotating the tooth. A. \(F_{1y}=-1.7\ \mathrm N, F_{2y}=3.5\ \mathrm N\) B. \(F_{1y}=-3.8\ \mathrm N,F_{2y}=5.6\ \mathrm N\) C. \(F_{1y}=-0.23\ \mathrm N, F_{2y}=2.0\ \mathrm N\) D. \(F_{1y}=4.0\ \mathrm N,F_{2y}=-2.2\ \mathrm N\) ________________ Equation Transcription: Text Transcription: F_{1y} F_{2y} 0.009 N{cdot}m F_{1y}=-1.7 N, F_{2y}=3.5 N F_{1y}=-3.8 N,F_{2y}=5.6 N F_{1y}=-0.23 N, F_{2y}=2.0 N F_{1y}=4.0 N,F_{2y}=-2.2 N

Suppose the mass of the pulley is doubled, to 0.160 kg, and that everything else in the system remains the same. (a) Do you expect the value of \(T_2\) to increase, decrease, or stay the same? Explain. (b) Calculate the value of \(T_2\) for this case. ________________ Equation Transcription: Text Transcription: T_2 T_2

Problem 115GP A mass M is attached to a rope that passes over a disk-shaped pulley of mass m and radius r. The mass hangs to the left side of the pulley. On the right side of the pulley, the rope is pulled downward with a force F. Find (a) the acceleration of the mass, (b) the tension in the rope on the left side of the pulley, and (c) the tension in the rope on the right side of the pulley, (d) Check your results in the limits m ? 0 and m ??.

What is the value of the torque that corresponds to one of the forces being equal to zero? A. \(0.0023\ \mathrm {N\cdot m}\) B. \(0.0058\ \mathrm {N\cdot m}\) C. \(0.0081\ \mathrm {N\cdot m}\) D. \(0.017\ \mathrm {N\cdot m}\) ________________ Equation Transcription: Text Transcription: 0.0023 N{cdot}m 0.0058 N{cdot}m 0.0081 N{cdot}m 0.017 N{cdot}m

Suppose the child runs with a different initial speed, but that everything else in the system remains the same. What initial speed does the child have if the angular speed of the system after the collision is 0.425 rad/s.

Problem 122IP Suppose the mass of the cart is doubled, to 0.62 kg, and that everything else in the system remains the same. (a) Do you expect the value of T 2 to increase decrease, or stay the same? Explain. (b) Calculate the value of T 2 for this case.

The two, solid straight lines in Figure 11–50 (b) represent the two forces applied to the tooth. Which line corresponds to which force? A. \(\mathrm I=F_{1y},\mathrm {II}=F_{2y}\) B. \(\mathrm I=F_{2y},\mathrm {II}=F_{1y}\) ________________ Equation Transcription: Text Transcription: I=F_{1y},II=F_{2y} I=F_{2y},II=F_{1y}

Problem 6P At the local playground, a 16-kg child sits on the end of a horizontal teeter-totter, 1.5 m from the pivot point. On the other side of the pivot an adult pushes straight down on the teeter-totter with a force of 95 N. Tn which direction does the teeter-totter rotate if the adult applies the force at a distance of (a) 3.0 m, (b) 2.5 m, or (c) 2.0 m from the pivot?

Problem 80P To prepare homemade ice cream, a crank must be turned with a torque of 3.95 N· m. How much work is required for the complete turn of the crank?

Problem 45P A baseball bat balances 71.1 cm from one end. If a 0, 560-kg glove is attached to that end, the balance point moves 24.7 cm toward the glove. Find the mass of the bat.

Problem 51P A uniform meterstick of mass M has an empty paint can of mass m hanging from one end. The meterstick and the can balance at a point 20.0 cm from the end of the stick where the can is attached. When the balanced stick-can system is suspended from a scale, the reading on the scale is 2.54 N. Find the mass of (a) the meterstick and (b) the paint can.