If a mass shrinks to half of its size then how many times does it’s rotational velocity increase by?

Short answer: it increases by a factor of 4.

Here’s why (under the usual physics assumptions):

• If no external torque acts, angular momentum is conserved.
• Angular momentum , where is the moment of inertia and is the rotational (angular) velocity.
• For most objects, (mass distribution scales with size squared).

So if the object shrinks to half it’s size:

To keep constant:

Angular momentum L = I * w where I is moment of inertia and w is angular velocity.

For a typical object, I is proportional to r^2.

If the object shrinks to half its size:

r -> r/2

I -> (1/2)^2 * I = I/4

Since L stays constant:

I * w = constant

(I/4) * w_new = I * w_old

So:

w_new = 4 * w_old

Result: The rotational velocity increases by 4 times.

✅ Result

The rotational velocity increases by a factor of 4.

This is exactly the same physics behind:

• Ice skaters spinning faster when they pull their arms in
• Collapsing stars spinning up into pulsars