The angular momentum of a rotating system is directly proportional to its rotational speed (angular velocity). Therefore, if the rotational speed doubles, the angular momentum also doubles.

Here's why:

* Angular Momentum (L) = Moment of Inertia (I) x Angular Velocity (ω)

* Moment of Inertia (I) is a measure of how resistant an object is to changes in its rotation. It depends on the object's mass distribution.

* Angular Velocity (ω) is the rate of change of angular displacement, essentially how fast the object is rotating.

If the rotational speed (ω) doubles, and the moment of inertia (I) remains constant, then the angular momentum (L) must also double to maintain the equation.