a figures skater rotating at 5 rads with arms extended has a moment of inertia of 2.25 kg. if the arms are pulled in so the moment of inertia decrease to 1.8 what is the final angular speed

The final angular speed is 6.25 rad/s

Explanation:

Given;

initial angular speed, ω₁ = 5 rad/s

initial moment of inertia, I₁ = 2.25 kg.m²

Final moment of inertia, I₂ = 1.8 kg.m²

final angular speed, ω₂ = ?

Based on conservation of angular momentum, we will have the following expression;

ω₁I₁ = ω₂I₂

ω₂ = (ω₁I₁ ) / I₂

ω₂ = (5 x 2.25) / 1.8

ω₂ = 6.25 rad/s

Therefore, the final angular speed is 6.25 rad/s