) A rigid, massless rod has three particles with equal masses attached to it as shown in Figure. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t = 0. Find, in terms of m and d a) the moment of inertia of the system of three particles about the pivot, b) the torque acting on the system at t = 0, c) the angular acceleration of the system at t= 0, d) the linear acceleration of the particle labeled 3 at t = 0, e) the maximum kinetic energy of the system, f) the maximum angular speed reached by the rod, g) the maximum speed reached by the particle labeled 2.
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 rigid, massless rod has three particles with equal masses attached to it as shown in
Figure. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to
the rod through the point P and is released from rest in the horizontal position at t = 0.
Find, in terms of m and d
a) the moment of inertia of the system of three particles about the pivot,
b) the torque acting on the system at t = 0,
c) the
d) the linear acceleration of the particle labeled 3 at t = 0,
e) the maximum kinetic energy of the system,
f) the maximum angular speed reached by the rod,
g) the maximum speed reached by the particle labeled 2.
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