For the equation L = r x p, assuming that the implied rotation occurs around a central point.

**Premise 1: **

There is a force at all times directed from the point mass along the radius toward the centre of rotation (centripetal force).

**Premise 2: **

A change in the magnitude of radius is conducted by altering the magnitude of this force.

**Premise 3:**

There can be no component of this force perpendicular to the radius.

**Premise 4: **

In order to affect the magnitude of the component of momentum perpendicular to the radius, one must apply a parallel component of force (Newton’s first law).

**Deduction: **

A change in the magnitude of the radius cannot affect the magnitude of the component of momentum perpendicular to the radius.

**Conclusion:**

In the equation L = r x p, assuming that the implied rotation occurs around a central point, it is the magnitude of the component of momentum perpendicular to the radius that must be conserved when the magnitude of the radius changes.