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$_{new}$ = $\frac{2}{5} I _{i}$

K.E$_{i} = \frac{I_{i} w^{2} }{2}$ --- (i)
K.E$_{new} = \frac{I_{new}w^{2} }{2}$

Therefore, 
K.E$_{new} = \frac{2I_{i}w^{2} }{5*2}$ ----(ii)


Dividing i and ii,

$\frac{K.E_{new} }{K.E_{i} } = \frac{2}{5}$