$2.3.14.$ A medieval rotary hammer has a heavy head of mass $m$ at the end of a light rod of length $l$. It is brought from a horizontal to an almost vertical position by rotating it around an axis passing through the other end of the rod. What minimum work must be done to raise the hammer? Neglect friction in the axis.
Solution
The minimum work $A_{\text{min}}$ will be spent entirely on increasing the potential energy of the hammer head (which acts as the center of mass) to the height $h = l$: $$A_{\text{min}} = \Delta E_p = mgl$$
