A person of mass m stands at the edge of a circular platform of radius R and moment of inertia. A platform is at rest initially. But the platform rotate when the person jumps off from the platform tangentially with velocity u with respect to platfrom. Determine the angular velocity of the platform.

Explanation

Let the angular velocity of platform is `omega`. Then the velocity of person with respect to ground v.
`v_(mD)= v_(mG) - V_(DG)`
` u = v_(m) + omega R`
`v_(m) = u - omega R `
Now from angular momentum conservation
`L_(i) = L_(f)`
` 0 = mv_(m) R - I omega `
`rArr I omega = m (u - omega R) . R `
` rArr omega = (m u R)/(l + mR^(2))`