A uniform rod with mass M, length L, and moment of inertial with respect to the center of ML? is hinged at one end (point P) so that it can rotate, without friction, around a mass ICM 12 horizontal axis. The rod is initially held at rest forming an angle 0 with the vertical (see figure) and then released. P a) Find the moment of inertia Ip of the rod with respect to point P. b) Find the magnitude of the angular velocity of the rod when it passes through the vertical. c) Find the linear speed of the center of mass when it passes through the vertical position. Write your results in terms of M, L, 0, and g. Check the units/dimensions for each answer. |