A solid sphere of radius `2.45m` is rotating with an angular speed of `10 rad//s`. When this rotating sphere is placed on a rough horizontal surface then after sometime it starts pure rolling. Find the linear speed of the sphere after it starts pure rolling.

Explanation

m=20 kg, angular speed = `omega = 100 s^(-1), r = 0.25` m
M.I. of the cylinder about its own axis `= I = 1/2 mr^(2)`
Rotational K.E. = `1/2 xx 1/2 mr^(2) xx omega^(2)`
`=1/4 xx 20 xx (0.25)^(2) xx (100)^(2) = 3,125` J
Angular momentum `L = I omega`
`=1/2 mr^(2) xx omega = 1/2 xx 20 xx (0.25)^(2) xx 100 = 62.5` Js