Time Dilation - Angular Momentum - Mass

[kmarinas86]

Angular momentum must be conserved. Does that mean that if a particle travels at relative velocity to an observer that the decrease in apparent spin rate will be offset by the increase in mass causing the angular momentum to be constant?

[jtbell]

Angular momentum must be conserved. Does that mean that if a particle travels at relative velocity to an observer that the decrease in apparent spin rate will be offset by the increase in mass causing the angular momentum to be constant?

I think you're confusing the words "conserved" and "invariant". When a quantity is conserved, it maintains the same value at different times in the same reference frame. When a quantity is invariant, it has the same value when measured from different reference frames. Angular momentum is conserved but I don't think it's necessarily invariant. Certainly linear momentum is not invariant, although it is conserved.