In the angular momentum equation L = r x p, which one of the remaining variables’ magnitudes is correctly conserved when the magnitude of the radius changes?

Question

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. 

Comments

This is not graduate-level, voting to close.

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Are you proposing that an absolute proof that the laws of physics are flawed and require a change is something that should be dealt with at a level below graduate?

Answer 1

You must employ the equations of motion $\dot{{\bf{p}}}=\bf{F}$ in order to derive your conclusions. If there is no force perpendicular to the radius, then the corresponding part of momentum is conserved.

Comments

Such high-school level questions should not be answered on PO

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@Dilaton: Instead of downvoting my answers, I propose you to develop means for deleting such questions. No votes are necessary for that.

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So you agree with my conclusion then "the corresponding part of momentum is conserved" `so why do you word your reply as if you do not agree?