Question

Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping. Hence find kinetic energy for a solid sphere.

Answer 1

Total Rolling kinetic energy = Translational K. E. + Rotational K. E.

`=1/2 MV^2+1/2 Iomega^2`

But

`omega=V/R `

`"Total Rolling K.E" = 1/2 MV^2+1/2 I(V^2/R^2)`

`"for solid sphere" I=2/5 MR^2`

`"Total Rolling K.E."=1/2 MV^2+1/2 (2MR^2)/5(V^2/R^2)`

`=1/2 MV^2+1/5 MV^2`

`=7/10 MV^2`