Collapsing sun, new average rotation

[physics123456]

Homework Statement

the sun collapses to the size of the Earth (approximately 1/100 the original diameter), The current average rotation of the sun is approximately 30 days.

Homework Equations

what would be the new rotational period (time to spin once)?

The Attempt at a Solution

I know that in 30 days, the sun has to travel a distance of 2pi. But I don't understand how that would change if the sun had a smaller diameter...that's where I am confused.

 

[haruspex]

Homework Statement

the sun collapses to the size of the Earth (approximately 1/100 the original diameter), The current average rotation of the sun is approximately 30 days.

Homework Equations

what would be the new rotational period (time to spin once)?

The Attempt at a Solution

I know that in 30 days, the sun has to travel a distance of 2pi. But I don't understand how that would change if the sun had a smaller diameter...that's where I am confused.

What conservation law might be useful? (You'll need to make some assumption about the way it collapses, e.g. that every part of it is it one hundredth of its previous radius.)