A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be _________rad s - 1 .

Step-by-step solution

The angular momentum is given by L = I C M ω = 2 M R 2 ω 5 The total kinetic energy is E = 1 2 ( M v 2 + 2 M R 2 ω 2 5 ) The ratio of angular momentum and kinetic energy is L E = I C M ω 1 2 M v 2 + 1 2 · 2 5 M R 2 ω 2 = 2 5 M R 2 ω 7 10 M R 2 ω 2 ⇒ π 22 = 4 7 · 1 ω ⇒ ω = 4   rad   s - 1