A paddlewheel is made by attaching 4 thin uniform blades oflength L and massmo to the exterior of a solid wooden disk of massM and radius R. The paddlewheel isfree to spin about an axisthrough its center, on frictionless bearings. A particle pf mass m,moving horizontally at speed vo impinges on the outer edge of thevertically-alignedbottom blade of the stationary paddlewheel.Uniform gravity g is present.a) Determine the moment of inertia forthe paddlewheel with blades, before being hit by m,.b) Assume m, ismade of clay and sticks to the'blade. What is vo such thatthepaddlewheel almost rotates by 180 degrees (i.e. the blade withclay attached nearlyreaches the top) after the collision?c) Forpart b), determine the kinetic energy of the paddlewheelimmediately after thecollision (do not include the kinetic energyof the attached clay).d) Now assume that m, is made of steel andthus bounces (fully elastically) straightback after hitting theblade, with velocity -vo. What is the kinetic energy ofthepaddlewheel after the collision?
