A a paddle for a boat is constructed of a stick of length L and a "quartic"end piece. The end can be thought of as a uniform flat board of mass m that has beencut to form a quartic function given by y = x*, so that the length from the trough (i.e.,the y0 end of the function) to the tip is y = H. To simplify this a little, assumethat the stick is massless. This paddle is stood vertically upward on the stick endand attached to a hinge on the floor so that it is free to rotate in the in/out of thepage direction. When it is standing straight up that is an unstable equilibrium. A verysmall infinitesimal push is given to get the paddle moving and it swings downward undergravity (acceleration g).(a) When the paddle is standing vertically upward, what is the position of the centerof mass of the paddle?(b) What is the moment of inertia of the paddle for rotations in/out of the page aboutan axis through the center of mass?(c) What is the angular velocity of the paddle just before it hits the ground?HL

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