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.

A solid sphere of radius 2.45m is rotating with an angular speed of 10

1.	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.
Answer» Solution :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