Find the expression for the moment of inertia of a uniform, solid disk of mass M and radius R, rotated about an axis that goes through its center as shown in the diagram below. Hint: the moment of inertia of a thin ring is given by MR². Divide the disk into a series of rings of radius r, mass dm, and thickness dr, then integrate over the rings. Your expression should only depend on the variables M and R. G
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).
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