Question

If a young protostar with a disk is rotating and shrinking. how much faster is it rotating after its size has decreased by a factor of 4? (enter an integer, as in it will be rotating ________ times faster). (3 pts)

Answer 1

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.