6. DETAILS R₂ R₁ mo R A hanging weight, with a mass of m₁ = 0.355 kg, is attached by a rope to a block with mass m₂ = 0.855 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R₁ = 0.0200 m, and an outer radius of R₂ = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μ = 0.250. At the instant shown, the block is moving with a velocity of v₁ 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, and that the mass of the rope is negligible. = my MY NOTES ASK YOUR TEACHER (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. m/s

6. DETAILS R₂ R₁ mo R A hanging weight, with a mass of m₁ = 0.355 kg, is attached by a rope to a block with mass m₂ = 0.855 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R₁ = 0.0200 m, and an outer radius of R₂ = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μ = 0.250. At the instant shown, the block is moving with a velocity of v₁ 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, and that the mass of the rope is negligible. = my MY NOTES ASK YOUR TEACHER (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. m/s

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 71P: The reel shown in Figure P10.71 has radius R and moment of inertia I. One end of the block of mass m...

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Rigid rods of negligible mass lying along the y axis connect three particles (Fig. P10.18). The system rotates about the x axis with an angular speed of 2.00 rad/s. Find (a) the moment of inertia about the x axis, (b) the total rotational kinetic energy evaluated from 12I2, (c) the tangential speed of each particle, and (d) the total kinetic energy evaluated from 12mivi2. (e) Compare the answers for kinetic energy in parts (b) and (d). Figure P10.18
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 uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height h. (a) If they are released from rest and roll without slipping, which object reaches the bottom first? (b) Verify your answer by calculating their speeds when they reach the bottom in terms of h.
The reel shown in Figure P10.71 has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle and the incline are frictionless. The reel is wound counterclockwise so that the spring stretches a distance d from its unstretched position and the reel is then released from rest. Find the angular speed of the reel when the spring is again unstretched. Figure P10.71
Consider the disk in Problem 71. The disks outer rim hasradius R = 4.20 m, and F1 = 10.5 N. Find the magnitude ofeach torque exerted around the center of the disk. FIGURE P12.71 Problems 71-75
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) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges?
A baseball catcher extends his arm straight up to catch a fast ball with a speed of 40 m/s. The baseball is 0.145 kg and the catcher’s arm length is 0.5 m and mass 4.0 kg. (a) What is the angular velocity of the arm immediately after catching the ball as measured from the arm socket? (b) What is the torque applied if the catcher stops the rotation of his arm 0.3 s after catching the ball?
A student rides his bicycle at a constant speed of 3.00 m/s along a straight, level road. If the bikes tires each have a radius of 0.350 m, (a) what is the tires angular speed? (See Section 7.3.) (b) What is the net torque on each tire? (See Section 8.5.)
A solid cylinder of radius 10.0 cm rolls down an incline with slipping. The angle of the incline is 30 . The coefficient of kinetic friction on the surface is 0.400. What is the angular acceleration of the solid cylinder? What is the linear acceleration?
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.
Suppose a disk having massMtot and radius R is broken intofour equal parts (Fig. P13.10).What is the rotational inertia ofone-fourth of the disk aroundthe z axis shown? FIGURE P13.10