The initial angular velocity of the system is i 020 revs 126 rads and we find

The initial angular velocity of the system is i 020

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The initial angular velocity of the system is i = 0.20 rev/s = 1.26 rad/s, and we find the final angular velocity via conservation of angular momentum, as f = I i I f i = 370 130 (1.26 rad/s) = 3.6 rad/s. (b) The change in kinetic energy is KE f - KE i = 1 2 I f f 2 - 1 2 I i i 2 , or  = 1 2 (130 kg m 2 )(3.58 rad/s) 2 - 1 2 (370 kg m 2 )(1.26 rad/s) 2 = 540 J. This difference results from work done by the man on the system as he walks inward.
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A cylinder with moment of inertia I 1 rotates about a vertical, frictionless axle with angular velocity v i . A second cylinder, this one having moment of inertia I 2 and initially not rotating, drops onto the first cylinder. Because of friction between the surfaces, the two eventually reach the same angular velocity v f . (a) Calculate v f . (b) Show that the kinetic energy of the system decreases in this interaction and calculate the ratio of the final to the initial rotational energy.
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(a) From conservation of angular momentum for the system of two cylinders: 1 2 1 f i I I I or 1 1 2 f i I I I (b) 2 1 2 1 2 f f K I I and 2 1 1 2 i i K I so 2 1 1 2 2 1 1 2 1 1 2 1 2 1 2 which is less than 1 f i i i K I I I I K I I I I I .
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A puck of mass m is attached to a cord passing through a small hole in a frictionless, horizontal surface. The puck is initially orbiting with speed v i in a circle of radius r i . The cord is then slowly pulled from below, decreasing the radius of the circle to r . (a) What is the speed of the puck when the radius is r ? (b) Find the tension in the cord as a function of r .
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(a) sin180 0   r F rF Angular momentum is conserved. f i i i i i L L mrv mrv rv v r (b) 2 2 3 i i m rv mv T r r FIG. P11.49
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