A girl throws a stick of length .27 m and mass .18 kg into the air so that the center of mass rises vertically. At the moment it leaves her hand, the stick is horizontal and the speed of the end of the stick nearest to her is zero. When the center of mass reaches its highest point, the stick has made 31 complete revolutions. How long did it take the center of mass to reach its highest point?
I let moment of inertia = (1/3)ML^2 (rod with rotational axis through end). I assume the problem uses conservation of energy combined with basic kinematics.
The Attempt at a Solution
At start, the rod has KE .5mv^2, v being the upwards velocity of the center of mass, and rotational KE .5Iw^2. At its highest point, it has potential energy mgh and rotational KE .5Iw^2. I assume the rotational kinetic energy does not change as it goes up? So the translational kinetic energy must equal mgh. I just don't know how to use the other information to get the height or velocity of the center of mass.