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# 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. - Physics

Sum

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.

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#### Solution

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

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