Question

A uniform rod hinged at it's one end is allowed to rotate in vertical plane. Rod is given an angular velocity omega in its vertical position as shown in figure. The value of omega for which the force exerted by the hinge on rod is zero in this position

Answer 1

The angular velocity is  ω = √ 2g /L when hinge force is zero.

Explanation:

Angular velocity "ω" = ?

Hinge force = 0

As hinge force is zero so the only force that will act is mg.

Now Newton's second law of motion:

mg = ma (CM)

     = M(/L/2 ω^2)

Now ω = √ 2g /L

Thus the angular velocity is  ω = √ 2g /L when hinge force is zero.

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