Question

The rotational inertia of a collapsing spinning star changes to 2/5 its initial value. what is the ratio of the new rotational kinetic energy to the initial rotational kinetic energy (kenew / kei)?

Answer 1

Let K.E
`_(i)` be the intial K.E and K.E
`_(new)` be new K.E,

I
`_(new)` =
`(2)/(5) I _(i)`

K.E
`_(i) = (I_(i) w^(2) )/(2)` --- (i)
K.E
`_(new) = (I_(new)w^(2) )/(2)`

Therefore,
K.E
`_(new) = (2I_(i)w^(2) )/(5*2)` ----(ii)


Dividing i and ii,


`(K.E_(new) )/(K.E_(i) ) = (2)/(5)`