Consider a homogeneous rigid body with a non-uniform distribution of mass. The body is rotating about a fixed axis. Which of the following statements about the moments of inertia is correct? A) The principal axes of inertia will coincide with the axis of rotation. B) The moment of inertia about the axis of rotation will be the smallest possible. C) The moment of inertia about any axis parallel to the axis of rotation will be constant. D) The moment of inertia tensor will be diagonal, with all diagonal elements distinct. Choose the correct option and justify your choice.
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 homogeneous rigid body with a non-uniform distribution of mass. The body is rotating about a fixed axis. Which of the following statements about the moments of inertia is correct?
A) The principal axes of inertia will coincide with the axis of rotation.
B) The moment of inertia about the axis of rotation will be the smallest possible.
C) The moment of inertia about any axis parallel to the axis of rotation will be constant.
D) The moment of inertia tensor will be diagonal, with all diagonal elements distinct.
Choose the correct option and justify your choice.
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