A long, thin, massless rod of length L rotates in a vertical plane about a frictionless pivot point. At the end of the rod opposite the pivot point is a mass M. The rod is initially positioned at a point above the pivot point such that the rod makes an angle of ? with respect to the horizontal. The mass is released with a push, giving it an initial speed V0. Assume V0, L, and g are all known.
A] Find the speed of the mass at the bottom of the swing.
B] Does the answer to part A depend upon the direction of the initial push? Justify your answer to this.
C] At what point in the motion does the mass have its minimum speed and what is this speed? Note, there may be two separate cases to consider.