An interstellar cloud of gas and dust with a radius of 10⁵ AU rotates slowly,with its outer edge traveling at 10⁻³ km/s.How fast is the outer edge of the cloud rotating after it contracts to 100 AU? A) 10^-1 km/s B) 1 km/s C) 100 km/s D) 10³ km/s

Question

Quizplus · Accepted Answer

The conservation of angular momentum states that the product of radius and rotational velocity stays constant, i.e., R1V1 = R2V2. 
So, we have:
10⁵ AU × 10⁻³ km/s = 100 AU × V2 
Solving for V2 gives:
V2 = (10⁵ AU × 10⁻³ km/s)/100 AU = 1 km/s 
Therefore, the outer edge of the cloud rotates at 1 km/s after it contracts to 100 AU.

An Interstellar Cloud of Gas and Dust with a Radius