Question 4: An annulus of inner and outer radii Rị and R2 has a non-uniform surface mass density given by o = 0or where o is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 2. a) Find the moment of inertia of the rod about an axis passing through its center of mass (the origin). Express your result in terms of M (mass of the annulus) and R1 and R2. b) Check your result as R1 - 0 and R2 = 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).
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