particle P of mass 2m can slide along a smooth rigid straight wire. The wire has one of its points fixed at the origin ’O’, and is made to rotate in a plane through ’O’ with constant angular speed Ω. Show that r , the distance of P from O, satisfies the equation r ̈ − (Ω^2)*r = 0 Initially, P is at rest (relative to the wire) at a distance a from O. Find r as a function of t in the subsequent motion.
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).
A particle P of mass 2m can slide along a smooth rigid straight wire. The wire has one of
its points fixed at the origin ’O’, and is made to rotate in a plane through ’O’ with constant
angular speed Ω. Show that r , the distance of P from O, satisfies the equation
r ̈ − (Ω^2)*r = 0
Initially, P is at rest (relative to the wire) at a distance a from O. Find r as a function of t in the subsequent motion.
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