Afigure skater is spinning slowly with arms outstretched. she brings her arms in close to her body and her moment of inertia decreases by 1/2. her angular speed increases by a factor of

the angular velocity increase by a factor of 2

Explanation:

using the law of the conservation of the angular momentum

where is the inicial angular momentum and is the final angular momentum.

also, the angular momentum can be calculated by:

L = IW

where I is the inertia momentum and the W is the angular velocity.

so:

we know that then,

solving for :

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.