A particle of mass m is located at x = 1, y = 0, z=2. Find the tensor of inertia for the particle relative to the origin. The particle rotates about the z axis through a small angle a << 1 as shown below. Show that the moments of inertia are unchanged to second order in a but the products of inertia can change linearly with a.
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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