Conservation Laws (Linear & Angulat Momentum)

[M. next]

As we are being introduced to this new lesson, it gets difficult sometimes to indicate which component of either (linear or angular momentum) is conserved.
Is there a strict rule to help me indicate which is which? Hmm, if not, can you give me the logical way through it?

Thanks in advance,
M. next

 

[Doc Al]

Can you give a specific example of what's confusing you?

 

[M. next]

Hmm, let's suppose we have an infinetly charged cylinder except a FINITE gap as in the photo.
But as in general, how do you think about it?

 

[Doc Al]

Sorry, but I don't see what your example has to do with conservation of momentum.

 

[M. next]

Doc Al,
As any problem, what components [linear or angular momentum ones] will stay conserved as a point charge moves in the field of a volume charged cylinder except the gap (see figure).

Thanks anyways.

 

[medthehatta]

Linear momentum will be conserved in the directions in which there aren't any applied forces, and angular momentum will be conserved in the directions in which there aren't any applied torques.

Here's a suggestion in the case of electrostatics: try writing down the potential for the system and inspecting it for dependency on the coordinates. Since (electrostatic) force is the gradient of the potential, the directions that conserve linear momentum will be the ones whose coordinates fail to appear in the potential. (Because if they did, there would be a nonzero derivative with respect to them, which means there would be a force in that direction.)

I should mention that a mathematician would scold me at this point: that suggestion won't work in curvilinear coordinates (cylindrical coordinates, say), so you'd have to use Cartesian coordinates in this case.