A disc of moment of inertia 2 ~kg - m ^2 revolving with 8 rad / s is placed on another disc of moment of inertia 4 ~kg - m ^2 revolving 4 rad / s . What is the angular frequency of composite disc?

Step-by-step solution

Given that, moment of inertia of discs, I ₁=2 ~kg - m ^2, I ₂=4 ~kg - m ^2 Angular velocity of discs, ₁=8 rad / s , ₂=4 rad / s From angular momentum conservation principle, I ₁ ₁+ I ₂ ₂= ( I ₁+ I ₂ ) or 2 8+4 4=(2+4) or = 16+16 6 = 32 6 = 16 3 rad / s