Rotation questions

1) Planetary mechanism consists of three gears each of mass Mand radius r and arm OA which may be regarded as a uniform bar ofmass m. The gear 1 is fixed whereas gears 2 and 3 may be regardedas uniform solid disks. Find kinetic energy T of the whole systemfor the case where the arm rotates in horizontal plane withconstant angular velocity 2) A device for impact testing consistsof a 34-kg pendulum with mass center at G and with radius ofgyration about O of 620 mm. The distance b for the pendulum isselected so that the force on the bearing at O has the leastpossible value during impact with the specimen at the bottom of theswing. Determine b and calculate the magnitude of the total force Ron the bearing O an instant after release from rest at theta = 603) In an acrobatic stunt, man a of mass ma drops from a raisedplatform onto the end of the light but strong beam with a velocityv0 The boy of mass mb is propelled upward with a velocity vb For agiven ratio n =mb/ma determine b in terms of L to maximize theupward velocity of the boy. Assume that both man and boy act asrigid bodies.

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