A slender stick of length 'L' and mass 'M' is lying on a smooth table and is able to move freely. A short impulse 'P' is imparted to it at a distance 'D' from the center and at right angle to the axis of the stick. Find

1) Linear and angular velocity of the stick immediately after impulse.

2) Angular displacement of stick after 't' sec from impulse.

Question

A slender stick of length 'L' and mass 'M' is lying on a smooth table and is able to move freely. A short impulse 'P' is imparted to it at a distance 'D' from the center and at right angle to the axis of the stick. Find

1) Linear and angular velocity of the stick immediately after impulse.

2) Angular displacement of stick after 't' sec from impulse.

askIITianexpert IITDelhi · Answer

1.) Impulse P = Change in linear momentum = MV-0 = MV

V=P/M

Angular impulse PD = Change in angular momentum = Iω-0 = Iω

ω = PD/(1/2ML²)= 2PD/ML²

2.) Angular Displacement θ = ωt = 2PDt/ML² rad.

There is no friction so there is no external torque & hence no angular accⁿ.

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