Question

Calculate rotational `K.E.` of earth about its own axis, taking it to be a sphere of mass `6 xx 10^(24) kg` and radius `6400 km`.

Answer 1

`E = ?, M = 6 xx 10^(24) kg`,
`R = 6400 km = 6.4 xx 10^(6) m`
Earth completes one rotation about its axis in 1 day.
`:. omega =(2pi)/(T) = (2pi)/(24 xx 60 xx 60) rad//s`
`E = (1)/(2) I omega^(2) = (1)/(2) xx (2)/(5)MR^(2) omega^(2)`
`= (1)/(5) xx (6 xx 10^(24)(6.4 xx 10^(6)) xx (2pi)^(2))/((24 xx 60 xx 60))`
`= 2.6 xx 10^(29) J`