The rotational inertia of a collapsing spinning star changes to 1/6 its initial value. What is the ratio of the new rotational kinetic energy to the initial rotational kinetic energy

Explanation:

Let the initial rotational inertia be I and final rotational inertia be I / 6 .

Let the initial angular velocity be ω₁ and final angular velocity be ω₂.

Applying conservation of angular momentum law

I x ω₁ = I / 6 x ω₂

6 ω₁  = ω₂

initial rotational kinetic energy = 1/2 I x ω₁ ²

Final  rotational kinetic energy = 1/2 ( I / 6 ) x ω₂ ²

Final  rotational kinetic energy / initial rotational kinetic energy

= ( 1 / 6 ) x ω₂ ² / ω₁ ²

=  ω₂ ² / 6ω₁ ²

= 36 ω₁ ² / 6ω₁ ²

= 6 .