A spherical ball rolls on a table without slipping. Determine the percentage of its `K.E.` which is rotational. Moment of inertia of sphere `= (2//5) xx mass xx ("radius")^(2)`.

Explanation

Total energy `= K.E.` of translation
`+ K.E.` of rotation
`(1)/(2)mv^(2) + (1)/(2)I omega^(2)`
`E = (1)/(2)m v^(2) + (1)/(2) ((2)/(5) m r^(2)) omega^(2)`
`= (1)/(2)m v^(2) + (1)/(5)m v^(2) = (7)/(10)m v^(2)`
`(K.E. "of rotation")/("total energy") = (((1)/(2))I omega^(2))/(((7)/(10))m v^(2))`
`=(((1)/(5))m v^(2))/(((7)/(10))m v^(2)) =(2)/(7) = (2)/(7) xx 100% = 28.57 %`