A rod of length L forming an angle β with the vertical strikes a frictionless floor at A with a vertical velocity v1 and no angular velocity. Assuming that the impact at A is perfectly elastic, derive an expression for the angular velocity of the rod immediately after the impact.

Ans. angular velocity = (12 x v₁ x sinβ) / (L (3sin²β +1)) (clockwise)

Question

A rod of length L forming an angle &beta; with the vertical strikes a frictionless floor at A with a vertical velocity v1 and no angular velocity. Assuming that the impact at A is perfectly elastic, derive an expression for the angular velocity of the rod immediately after the impact. Ans. angular velocity = (12 x v 1 x sin&beta;) / (L (3sin 2 &beta; +1)) (clockwise)

SAGAR SINGH - IIT DELHI · Answer

Dear student,

Well draw out the shape it makes
then use moments to find the answer
the moments acting downwards
0.75x9.81x3.1xcos 40
that then is equal to the force acting upwards
Txcos X
where T is the tension in the string
and X is the angle between the string and the wall (find using pythagoras and trigonometry)

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