If a young protostar with a disk is rotating and shrinking. how much faster is it rotating after its size has decreased by a fac

Question

bearhunter [10]

3 years ago

11

If a young protostar with a disk is rotating and shrinking. how much faster is it rotating after its size has decreased by a fac

tor of 4? (enter an integer, as in it will be rotating ________ times faster). (3 pts)

Physics

1 answer:

maks197457 [2] · Answer 1 · 2022-03-24T22:08:30+03:00

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.