Derive expressions for the final velocity and total energy of a body rolling without slipping.

Explanation

A rolling body has both translational kinetic energy and rotational kinetic energy. So the total K.E energy of a rolling body is,
` K.E_(T) = K.E_("Translational") +K.E_("Rotational")`
`rArr K.E_(T) = 1/2mv^2 + 1/2Iomega^2`
`rArr K.E_(T) = 1/2 mv^2 +1/2mk^2 (v^2)/(r^2) " " [ because I = mk^2 " and " v = romega]`
total energy ` E = 1/2mv^2 p1+ k^2/r^2]`
`rArr v^2 = (2E)/(m[1+k^2/r^2])`
`therefore` Velocity of the body, ` v = sqrt((2E)/(m [1+k^2/r^2]))`