Two particles of masses m 1 and m 2 are connected by a rigid massless rod of length r to constitute a dumbbell which is free to move in a plane. Show that the moment of inertia of the dumbbell about an axis perpendicular to the plane passing through the center of mass is μr 2 where μ is the reduced mass.
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).
Two particles of masses m 1 and m 2 are connected by a rigid massless rod of length r to constitute a dumbbell which is free to move in a plane. Show that the moment of inertia of the dumbbell about an axis perpendicular to the plane passing through the center of mass is μr 2 where μ is the reduced mass.
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