Question

a uniform rod ab of mass m and length l is at rest on a smooth horizontal surface An impulse Is applied to the end Perpendicular to the rod in horizontal direction

Answer 1

mass = M

Length = L

Impulse = I

Time during which the impulse is given = t

Due to the impulse:

Change in linear momentum = I * t.

Change in angular momentum about the center of mass of the rod = I*t*L/2

The linear and angular momenta are conserved as the surface is frictionless.

Linear Speed of center of mass in the direction of impulse

= I t / M

Moment of inertia of thin rod about its center = M L^2/ 12

Angular velocity w of rod about center = I * t * L/2 ÷ (M L^2/12)

= 6 I t /(M L)