# How can a system of particles with kinetic energy have no momentum?

1. Nov 13, 2012

### Lo.Lee.Ta.

I thought objects with kinetic energy have to be moving...

And moving objects have momentum...

So how is it that something with kinetic energy can have no momentum?

Could you give me specific examples of such cases?

Thank you so much! :)

2. Nov 13, 2012

### Delphi51

If you mean the sum of the momentum of all the particles, it could be half of them going one way and half the opposite way so the total is zero.

3. Nov 13, 2012

### ehild

The momentum is vector, the KE is scalar.

A system of two particles, each of mas m and one with velocity v, the other with velocity -v, has momentum mv-mv=0 and kinetic energy mv2/2+m(-v)2/2=mv2.

ehild

4. Nov 13, 2012

### Lo.Lee.Ta.

Oh! I didn't even think of that! Okay, so there can be particles with negative momentum and others with positive momentum of equal magnitude, and they can cancel each other out?

5. Nov 13, 2012

### ehild

In general, the momentum can be of any direction, and their vector sum can cancel, but the KE is positive for all particles.

ehild

6. Nov 13, 2012

### Lo.Lee.Ta.

Oh, okay! Thank you ehild and Delphi51! :)