Calculate rotational kinetic energy, power and energy loss, then relate moment of inertia, angular speed, angular momentum and conservation of energy.
A student models a rotating dancer using a system that consists of a vertical cylinder, a horizontal rod and two spheres.
The cylinder rotates from rest about the central vertical axis. A rod passes through the cylinder with a sphere on each side of the cylinder. Each sphere can move along the rod. Initially the spheres are close to the cylinder.
A horizontal force of 50 N is applied perpendicular to the rod at a distance of 0.50 m from the central axis. Another horizontal force of 40 N is applied in the opposite direction at a distance of 0.20 m from the central axis. Air resistance is negligible.
When the system has reached its maximum angular speed, the two forces are removed. The spheres now move outward, away from the central axis.
Show that the rotational kinetic energy is where L is the angular momentum
of the system.