Question

A rigid rod (mass = 3 kg, L=1.5m) is free to rotate on a

frictionless pivot (see diagram). If the rod is released from rest in the

horizontal position shown with point A at the free end of the rod,

(a) What is the linear acceleration of point A when the rod is first

released?

(b) What is the angular velocity of point A when it reaches the

position indicated by the dashed line?

Answer 1

a)

When the rod is released from horizontal position,

Initial angular velocity of rod is zero,

The point A has only tangential acceleration, , radial acceleration

Linear acceleration of point A is

Net torque on the rod about the pivot, (the only force acting is rods weight at a distance from pivot)

( moment of inertia of rod rotating at one end is )

Linear acceleration of point A is

b) When rod is in vertical position,

Conserving the energy of rod ,