Question

A thin uniform rod of mass m and length l is free to rotate about its upper end. When it is at rest, it receives an impulse J at its lowest point, normal to its length. Immediately after impact, 

(a) the angular momentum of the rod is Jl 

(b) the angular velocity of the rod is 3J/ml 

(c) the kinetic energy of the rod is 3J²/ 2m 

(d) the linear velocity of the midpoint of the rod is 3J/2m

Answer 1

Correct Answer is: (a, b, c, & d)

Angular momentum = linear momentum x perpendicular distance from the point of rotation

or L = Jl

Also, I = ml²/ 3.

∴ ω =  L/I = 3J/ml.

Kinetic energy = L² /2I = J²l² / 2(ml² / 3) = 3J²/2m

v_c = ω. l/2 =3J/2m.