1) Planetary mechanism consists of three gears each of mass M and radius r and arm OA which may be regarded as a uniform bar of mass m. The gear 1 is fixed whereas gears 2 and 3 may be regarded as uniform solid disks. Find kinetic energy T of the whole system for the case where the arm rotates in horizontal plane with constant angular velocity 2)

A device for impact testing consists of a 34-kg pendulum with mass center at G and with radius of gyration about O of 620 mm. The distance b for the pendulum is selected so that the force on the bearing at O has the least possible value during impact with the specimen at the bottom of the swing.

Determine b and calculate the magnitude of the total force R on the bearing O an instant after release from rest at theta = 60 3) In an acrobatic stunt, man a of mass ma drops from a raised platform onto the end of the light but strong beam with a velocity v0 The boy of mass mb is propelled upward with a velocity vb For a given ratio n =mb/ma determine b in terms of L to maximize the upward velocity of the boy. Assume that both man and boy act as rigid bodies.