If 2 ~kg mass is rotating on a circular path of radius 0.8 ~m with angular velocity of 44 rad / sec . If radius of the path becomes 1 ~m , then what will be the value of angular velocity?

Step-by-step solution

Mass (m)=2 ~kg ; initial radius of the path (r₁ )=0.8 ~m ; initial angular velocity ( ₁ )=44 rad / sec and final radius of the path (r₂ )=1 ~m Moment of inertia, I₁=m r₁^2=2 (0.8)^2=1.28 ~kg ~m ^2 and I₂=m r₂^2=2 (1)^2=2 ~kg m ^ 2 Therefore from the law of conservation of angular momentum I₁ ₁=I₂ ₂ or ₂= I₁ ₁ I₂ = 1.28 44 2 ₂=28.16 rad / sec