A uniform circular disc of mass m is set rolling on a smooth horizontal table with a uniform linear velocity v. Find the total K.E., of the disc.

Explanation

M.I. of th disc about its own axios,
Formula, `I=1/2 mr^(2)`
As `v=r omega: omega^(2)=(v^(2))/(r^(2))`
Rotational K.E. `=1/2 I omega^(2)`
`=1/2xx1/2mr^(2)xx(v^(2))/(r^(2))=1/4 mv^(2)`
Translational K.E. `=1/2mv^(2)`
Total K.E. `=` Rotaltional K.E.+Translational K.E
`=1/4mv^(2)+1/2 mv^(2)`
`=3/4 mv^(2)`