Angular momentum and when center of rotation is changed

[Strang]

Hello.

The problem is this, what happens to angular momentum, tangential velocity and centripetal force when you change the center of rotation.
For example, if we have rotating hinged arm, weight at the end, with certain angular momentum and tangential speed etc. which then gets stopped at hinge, but the 2nd part of the hinge can still rotate thus giving half the radius and a different center of rotation.

Normaly, if you decrease radius (for example weight at the end of the string and you pull the string decreasing radius) you can assume there´s no torque and because of that L=mrv, L/m=rv and from there see that radius and velocity are inversely proportionate.

As far as i know the angular momentum is always relative to center of rotation, so when the center of rotation shifts, can you still use the above formula and others like it, or does something weird happen? Intuition says it´s the same, but i haven´t been able to find proper source to prove it. So does anyone know a site/book/thing where it´s discussed?

 

[Comeback City]

Angular momentum has to be conserved, but I guess it depends on how you "change" the center of rotation.

As far as i know the angular momentum is always relative to center of rotation, so when the center of rotation shifts, can you still use the above formula and others like it, or does something weird happen?

If the system is moving in constant uniform motion, then nothing weird would happen. But if you apply a force to accelerate the system, it would probably change.

 

[Khashishi]

Angular momentum is different around different pivots.
You can decompose the total angular momentum into a rotation around the center of mass (classical spin angular momentum) and an orbital angular momentum. The spin part of the angular momentum stays the same when you shift around the pivot, but the orbital part will change, since that part is given by
$\mathbf{L}_o = \mathbf{R}_{cm} \times \mathbf{P}_{cm}$

 

[Khashishi]

To clarify, total angular momentum is conserved in any inertial reference frame, measured relative to the origin of the inertial reference frame. It has different values in different inertial reference frames.

You should measure angular momentum with respect to the origin of a reference frame, not with respect to the joints in a system (which may be moving in a non-inertial motion).