IB Physics Rod Swinging in a Vertical Plane

This tutorial sheet is about a uniform rod swinging in a vertical plane.

A uniform rod of length 2L mass M can swing freely in a vertical plane about a horizontal axis through one end. The rod is released from rest when it is horizontal.

1. What are the acceleration components of the end of the rod when it makes an angle 𝜃 with the vertical?
2. Find the magnitude of the force exerted by the point of support of the rod when it makes an angle 𝜃 with the vertical.
3. Draw a graph showing the angular speed of the rod in terms of the angle that the rod makes with the vertical.
4. The rod is now released from the horizontal position and is given an initial angular speed. Find the least initial angular speed that will allow the rod to complete a full revolution.