What does it mean for momentum to be a constant of motion?

[jus8727]

what does it mean for momentum to be constant of motion.
i know that if it is it will commute with the hamiltonian but what does it mean in words?

 

[jdwood983]

If momentum is a constant of motion, there's a couple of things it means:

(1) momentum is conserved--the total momentum of the system (at least in the particular direction/angle) is constant
(2) the time derivative of momentum is zero ($\dot{p}=0$)--this does not mean there is no motion, just that the time-evolution of the motion is non-existent.

You should look at "[URL Theorem[/url] and http://en.wikipedia.org/wiki/Constant_of_motion" . These wiki articles might help you understand more.