Consider a rotating disk of radius R that has the exotic property that it can change its mass per unit area as a function of r. Initially, its mass per unit area is given by ar3, where a is a constant. What is the moment of inertia of this disk expressed in terms of its mass, M and radius R.
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).
Consider a rotating disk of radius R that has the exotic property that it can change its mass
per unit area as a function of r. Initially, its mass per unit area is given by ar3, where a is a
constant.
What is the moment of inertia of this disk expressed in terms of its mass, M and
radius R.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
