3. A 75 g, 30 cm long rod hangs vertically on a friction less, horizontal axel passing through the center. A 10 g ball of clay travelling horizontally at 2.5 m/s hits and stick to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod rotates when the ball of clay is attached to the rod? just how to approach for the problem

Question

3.	A 75 g, 30 cm long rod hangs vertically on a friction less, horizontal axel passing through the center. A 10 g ball of clay travelling horizontally at 2.5 m/s hits and stick to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod rotates when the ball of clay is attached to the rod? just how to approach for the problem

anonymous · Answer

torque = r x f = r m g sin(theta). integral(torque dtheta)=work=the initial angular energy (since the rod comes to a full stop)=L^2/(2I). L=r m v. Thus g(1-cos(theta))=r m v^2/(2I).