Initial angular velocity of a circular disc of mass M is ω1 Then two spheres of mass m are attached gently two diametrically opposite points on the edge of the disc what is the final angular velocity of the disc?
Answer & explanation
Correct answer: option 3
Conservation of Angular Momentum : I1ω1 = I2ω2
ω2 = (I1 / I2)ω1
For circular disc : I = [(MR2) / 2]
I1 = [(MR2) / 2]
when two spheres of masses are attached then total mass is M + 2m
I2 = [(M + 2m) / 2]R2
hence ω2 = [{(MR2) / 2} / {{(M + 2m) / 2}]R2}](ω1)
= [M / (M + 2m)]ω1