In this system we have the conservation of angular momentum: L₁ = L₂
We can write L = m·r²·ω
Therefore, we will have:
m₁ · r₁² · ω₁ = m₂ · r₂² · ω₂
The mass stays constant, therefore it cancels out, and we can solve for ω₂:
ω₂ = (r₁/ r₂)² · ω₁
Since we know that r₁ = 4r₂, we get:
ω₂ = (4)² · ω₁
= 16 · ω₁
Hence, the protostar will be rotating 16 times faster.
