a) A solid cylindrical pulley with a radius of 15.0 cm is spinning at a rate of4

Question

a) A solid cylindrical pulley with a radius of 15.0 cm is spinning at a rate of45.0 rpm. If the mass of the pulley is 30.0 kg, what is the pulley's angular momentum? b) The pulley's radius shrinks steadily to a new radius of 10.0 cm over a time interval of 5.00 seconds. What the new gular momentum? What is the net amount of torque that must have been to cause change in angular momentum? c) Assuming the force causing the torque was exerted tangentially on the pulley's surface, what size force would be needed to cause this change in angular momentum? Part 2: Conservation of Angular Momentum Ingally related to the mass of the rotating object as well as iti md

Explanation / Answer

moment of inertia of cylinder = 0.5 * MR^2

moment of inertia of cylinder = 0.5 * 30 * 0.15^2

moment of inertia of cylinder = 0.3375 kg.m^2

angular velocity = 45 rpm or 4.712 rad/sec

angular momentum = moment of inertia * angular velocity

angular momentum = 0.3375 * 4.712

angular momentum = 1.5903 kg-m^2/sec

when radius is shrunked

angular momentum = 0.5 * 30 * 0.1^2 * 4.712

angular momentum = 0.7068 kg-m^2/sec

torque = change in angular momentum / time

torque = (1.5903 - 0.7068) / 5

torque = 0.1767 Nm

torque = force * radius

0.1767 = force * 0.1

force = 1.767 N

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