M, L 60°
A thin uniform rod of mass Mr and length L is suspended from the ceiling and mounted on a horizontal frictionless axle at the top. The rod is initially at rest in its equilibrium position when a ball of playdough, of mass mb,strikes the rod at its lower endand remains stuck to the rod. The sticky ball is thrown with an initial speed v0at a 60 degree angle from the horizontal direction, and strikes the rod when it reaches the top of its trajectory, as shown in Fig.4. The acceleration due togravity has magnitude g and air resistance is negligible.
a)Determine the velocity of the ball of play dough right before it sticks to the rod. Use the x-y coordinate system defined in Fig.4.
b)Determine the angular velocity of the rod+ball system right after the collision. Take counterclockwise as positive.
c)Establish the differential equation satisfied by the rod+ball system after the collision and determine the angular frequency of the system. You may assume that the small angle approximation (sin≈) is valid.
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