A mass attached at the end of a massless string swings around in a horizontal
circle (the string sweeps out a cone). Let ? be the angle the string makes with
the vertical, l be the length of the string, h is the vertical height of the string,
and r is the radius of the circle. So, l is the hypotenuse of a right triangle with
h and r as legs, and ? as the upper angle. The length of the string l is slowly
increased (or decreased).
(a) Assuming that ? is very small, how does r depend on l?
(b) Assuming that ? is very close to ?/2, how does h depend on l?
You will need to consider angular momentum as well as Newton’s 2nd.