Consider this problem: A mass is in circular motion, held by a string, at radius Ro with angular velocity Wo. Then, the string is pulled towards the center with speed Vo, so the radius is decreasing at a rate Vo. What is the angular velocity of the mass as a function of time? The problem is trivial to solve using conservation of angular momentum. I'm trying to solve it without resorting to angular momentum, but I'm a bit lost. The tangential velocity is increasing, which confused me at first, but after thinking, i figured that the Vo bleeds off into the tangential velocity. Is this correct?