A solid sphere of radius R = 2.0 m, mass M = 10 kg, and moment of inertia I = (2/5)MR^2 is initially at rest in the position shown, with h = 8 m, and is released and rolls down the plane without slipping. When the sphere reaches the bottom of the inclined plane:
a) Determine its translational speed v.
b) Determine its angular speed ω.
c) Determine its rotational kinetic energy KE_rot.
In the frictionless system shown below, both pulleys have the same mass and radius (M = 4 kg and R = 2 m). However, the pulley on the right is a hoop with moment of inertia I = MR^2 while the pulley on the left is a disk with moment of inertia I = (1/2)MR^2. The system is released from rest.
Determine the velocity of the 100 kg block at the moment it has descended 6 meters.