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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.
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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