Question

Jae dropped an object from an inclined plane. The angle of the inclined plane with respect to the horizontal direction is 30 degrees and the distance from where the object was dropped to the surface of the Earth in a vertical direction is 100 meters. Assuming that the object is a solid sphere and it is going to move with a certain angular velocity as it moves down the inclined plane and there is no frictional force that we need to worry about, calculate the final velocity of the object just before it hits the surface.

Answer 1

Height of the point at which the solid sphere is dropped,  

Total kinetic energy (KE) of the sphere = KE due to rotation+ KE due to translation

where, is the mass, is the translational velocity, the angular velocity and is the moment of inertia and are given by

where is the radius of the sphere.

Since the sphere started at rest and avoiding frictional losses

Total KE when it hits the surface = Total potential energy at the top

That is