8: A sphere, I= 0.45 kg m' and r= 8 cm, is initially rotating at 22 rad/s. You put your hand on the sphere at point P and slow the disk to 4 rad/s while it rotates 7.2 times. A: Using the work energy theorem, what is the magnitude of the applied force? Axis of rotation 30 B: Where on the sphere would to apply the force to get maximum torque. Use equations to justify your

8: A sphere, I= 0.45 kg m' and r= 8 cm, is initially rotating at 22 rad/s. You put your hand on the sphere at point P and slow the disk to 4 rad/s while it rotates 7.2 times. A: Using the work energy theorem, what is the magnitude of the applied force? Axis of rotation 30 B: Where on the sphere would to apply the force to get maximum torque. Use equations to justify your

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 125CP: A cord is wrapped around the rim of a solid cylinder of radius 0.25 m, and a constant force of 40 N...

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While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. (a) Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900kg-m2 the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. (b) How much work is done if the leg rotates through an angle of 20.0° with a constant force exerted by the muscle?
A cord is wrapped around the rim of a solid cylinder of radius 0.25 m, and a constant force of 40 N is exerted on the cord shown, as shown in the following figure. The cylinder is mounted on frictionless bearings, and its moment of inertia is 6.0kgm2 . (a) Use the work energy theorem to calculate the angular velocity of the cylinder after 5.0 m of cord have been removed. (b) If the 40-N force is replaced by a 40-N weight, what is the angular velocity of the cylinder after 5.0 m of cord have unwound?
A uniform cylindrical grindstion has a mass of 10 kg and a radius of 12 cm. (a) What is the rotational kinetic energy of the grindstone when it is rotating at 1.5103rev/min ? (b) After the grindstone’s motor is turned off, a knife blade is pressed against the outer edge coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.
A uniform disk of mass 500 kg and radius 0.25 m is mounted on frictionless bearings so it can rotate freely around a vertical axis through its center (see the following figure). A cord is wrapped around the rim fo the disk and pulled with a force of 10 N. (a) How much work has the force done at the instant the disk has completed three revolutions, starting from rest? (b) Determine the torque due to the force, then calculate the work done by this torque at the instant the disk has completed three revolutions? (c) What is the angular velocity at the instant? (d) What is the power output of the force at that instant?
Consider two objects with m1 m2 connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation as shown in Figure P10.44. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this time.
As shown in Figure OQ10.7, a cord is wrapped onto a cylindrical reel mounted on a fixed, friction less, horizontal axle. When does the reel have a greater magnitude of angular acceleration? (a) When the cord is pulled down with a constant force of 50 N. (b) When an object of weight 50 X is hung from the cord and released, (c) The angular accelerations in parts (a) and (b) are equal, (d) It is impossible to determine.
The puck in Figure P11.46 has a mass of 0.120 kg. The distance of the puck from the center of rotation is originally 40.0 cm, and the puck is sliding with a speed of 80.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Suggestion: Consider the change of kinetic energy.) Figure P11.46
A competitive diver leaves the diving board and falls toward the water with her body straight and rotating slowly. She pulls her arms and legs into a tight tuck position. What happens to her rotational kinetic energy? (a) It increases. (b) It decreases. (c) It stays the same. (d) It is impossible to determine.
A tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.03 m/s on a horizontal section of a track as shown in Figure P10.62. It rolls around the inside of a vertical circular loop of radius r = 45.0 cm. As the ball nears the bottom of the loop, the shape of the track deviates from a perfect circle so that the ball leaves the track at a point h = 20.0 cm below the horizontal section. (a) Find the balls speed at the top of the loop. (b) Demonstrate that the ball will not fall from the track at the top of the loop. (c) Find the balls speed as it leaves the track at the bottom. What If? (d) Suppose that static friction between ball and track were negligible so that the ball slid instead of rolling. Would its speed then be higher, lower, or the same at the top of the loop? (e) Explain your answer to part (d). Figure P10.62
(a) Calculate the rotational kinetic energy of Earth on its axis. (b) What is the rotational kinetic energy of Earth in its orbit around the Sun?
A cord is wrapped around a pulley that is shaped like a disk of mass m and radius r. The cords free end is connected to a block of mass M. The block starts from rest and then slides down an incline that makes an angle with the horizontal as show n in Figure P10.48. The coefficient of kinetic friction between block and incline is . (a) Use energy methods to show that the blocks speed as a function of position d down the incline is v=4Mgd(sincos)m+2M (b) Find the magnitude of the acceleration of the block in terms of , m, M, g, and . Figure P10.48
A disk with moment of inertia I1 rotates about a frictionless, vertical axle with angular speed i. A second disk, this one having moment of inertia I2 and initially not rotating, drops onto the first disk (Fig. P10.50). Because of friction between the surfaces, the two eventually reach the same angular speed f. (a) Calculate f. (b) Calculate the ratio of the final to the initial rotational energy. Figure P10.50