Question

A wodden log mass `M` and length `L` is hinged by a frictionless nail at `O.A` bullet of mass `m` strikes with velocity `v` and strikes with velocity `v` and sticks to it . Find angular velocity of the system immediately after after the collision about `O`.
.

Answer 1

Correct Answer - `omega = (3mv)/((3m + M) L)`
Angular momentum of the system about point `O` will remain conserved.
`L_(i) = L_(f)`
`mvL = I omega rArr mvL = [mL^(2) + (ML^(2))/(3)) omega`
`omega = (3mv)/(L(3 m + M))`.