consider this figure very very carefully. lets say that circle is rollin around that whole platform lol. this circle (or should we say a real solid robust ball of some sort, lets just call it that way) starts from rest. r = radius of this circle (or robust ball solid) R = radius of this platform lets assume this ball/circle stays on the platform and doesnt slip at all. we need to find the speed of this one as it goes thru the lowest point of the platform, as it starts from this angle shown in the figure.

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Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).