Question

A spherical ball of radius `r` and mass `m` is rolling without slipping on a horizontal table. Calculate the percentage of `KE`, which is translational.

Answer 1

Total `KE = KE` of translation `+ KE` of rotation
`E = (1)/(2) mv ^(2) + (1)/(2)I omega^(2)`
Now, for the ball, `I = (2)/(5)m r^(2)`
`:. E = (1)/(2) m v^(2) + (1)/(2) xx (2)/(5) m r^(2) omega^(2)`
`E = (1)/(2)m v^(2) + (1)/(2) m v^(2) = (7)/(10) m v^(2)`
`(E_("translational"))/(E_("total")) = ((1)/(2)m v^(2))/((7)/(10) m v^(2)) = (10)/(14) = (5)/(7)`
`= (5)/(7) xx 100% = 71.4%`