Consider a light rod of length l with its upper end clamped such that it is free to rotate. A small heavy block is attached to its lower end. What is the minimum horizontal velocity that must be imparted to the block for it to travel in a complete vertical circle?

Step-by-step solution

For a block attached to a light rod, the rod can provide both tension and compression. Thus, the rod will not slacken like a string. To complete the vertical circle, the minimum velocity at the highest point can be zero, i.e., v_ top = 0 . Using conservation of mechanical energy between the lowest and highest points: 1 2 mv^2 = 1 2 mv_ top ^2 + mg(2l) Substituting v_ top = 0 : 1 2 mv^2 = mg(2l) v^2 = 4gl v = 2 gl