A solid brass ball of mass 22 g and radius 8.51 mm rolls smoothly along a loop-the-loop track when released from rest from a tall ramp leading to the loop-the-loop. The circular loop has a 17 cm radius. (a) What is the minimum height from which you can release the ball so that it will go around the loop-the-loop without falling off? For part (b), assume that the ball is released from rest at a height of 61.83 cm above the bottom of the loop. (b) What is the magnitude of the horizontal force on ball when it is at a height 17 cm going up the hoop? (c)What is the direction of the net force on the ball at the top of the hoop? ]ŷ

A solid brass ball of mass 22 g and radius 8.51 mm rolls smoothly along a loop-the-loop track when released from rest from a tall ramp leading to the loop-the-loop. The circular loop has a 17 cm radius. (a) What is the minimum height from which you can release the ball so that it will go around the loop-the-loop without falling off? For part (b), assume that the ball is released from rest at a height of 61.83 cm above the bottom of the loop. (b) What is the magnitude of the horizontal force on ball when it is at a height 17 cm going up the hoop? (c)What is the direction of the net force on the ball at the top of the hoop? ]ŷ

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 83P: A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.83....

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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.
A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.83. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? (b) What are the force components on the sphere at the point P if h = 3R? Figure P10.83
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 P10.33. 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. (d) What If? Suppose that static friction between ball and track were negligible so that the ball slid instead of rolling. Describe the speed of the ball at the top of the loop in this situation. (e) Explain your answer to part (d). Figure P10.33
A turntable (disk) of radius r = 26.0 cm and rotational inertia0.400 kg m2 rotates with an angular speed of 3.00 rad/s arounda frictionless, vertical axle. A wad of clay of mass m =0.250 kg drops onto and sticks to the edge of the turntable.What is the new angular speed of the turntable?
In testing an automobile tire for proper alignment, a technicianmarks a spot on the tire 0.200 m from the center. He then mountsthe tire in a vertical plane and notes that the radius vector to thespot is at an angle of 35.0 with the horizontal. Starting from rest,the tire is spun rapidly with a constant angular acceleration of 3.00 rad/s2. a. What is the angular speed of the wheel after 4.00 s? b. What is the tangential speed of the spot after 4.00 s? c. What is the magnitude of the total accleration of the spot after 4.00 s?" d. What is the angular position of the spot after 4.00 s?
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
A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.
A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm (see below). The system rotates about an axis through the center of the disk and annular cylinder at 10 rev/s. (a) What is the moment of inertia of the system? (b) What is its rotational kinetic energy?
A space station is constructed in the shape of a hollow ring of mass 5.00 104 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (See Fig. P10.52.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. (a) What angular momentum does the space station acquire? (b) For what time interval must the rockets be fired if each exerts a thrust of 125 N? Figure P10.52 Problems 52 and 54.
An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley that is rigidly attached to the flywheel as shown in Figure P10.37. The flywheel is a solid disk with a mass of 80.0 kg and a radius R = 0.625 m. It turns on a frictionless axle. Its pulley has much smaller mass and a radius of r = 0.230 m. The tension Tu in the upper (taut) segment of the belt is 135 N, and the flywheel has a clockwise angular acceleration of 1.67 rad/s2. Find the tension in the lower (slack) segment of the belt. Figure P10.37
A hollow cylinder that is rolling without slipping is given a velocity of 5.0 m/s and rolls up an incline to a vertical height of 1.0 m. If a hollow sphere of the same mass and radius is given the same initial velocity how high vertically does it roll up the incline?
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