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.

A uniform circular disc of mass m is set rolling on a smooth horizonta

1.	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.
Answer» Solution :Total K.E. = Translational K.E. + ROTATIONAL K.E. `=1/2 mv^(2) + 1/2 IOMEGA^(2)` For a disc `I = 1/2 mr^(2), v = r OMEGA, omega^(2) = v^(2)/r^(2)` Total K.E. `=1/2 mv^(2) + 1/2 xx 1/2 mr^(2) xx v^(2)/r^(2) =1/2 mv^(2) + 1/4 mv^(2) = 3/4 mv^(2)`