# Homework Help: Difference between kinetic energy and momentum

1. Nov 8, 2009

### Jeff5738

Not exactly a homework question, so sorry if I'm in the wrong forum

1. The problem statement, all variables and given/known data

I'm trying to understand the difference between KE and momentum.

2. Relevant equations

It seems to me that:
In a collision, KE can be converted into heat, which is a kind of KE/potential energy because it is the vibration of atoms: ie, energy is conserved, but it can change into a different kind of energy.

But what about momentum? As far as I understand, momentum is always conserved, even in inelastic collisions. But if some of the KE has become heat after a collision, why can't some of the momentum become heat, too. Or don't vibrating atoms have momentum?

3. The attempt at a solution

OK. Maybe I'm seeing a possible answer here: because those atoms are vibrating randomly in different directions, the aggregate momentum of the body warmed after the collision does not change due to the warming. Momentum can't be changed into heat and the body has to change its overall motion instead.

Is this right?

2. Nov 8, 2009

### Seannation

It's quite hard to conceptualise but the difference can be shown by remembering that energy is a scalar quantity and momentum is a vector quantity. In a collision, due to Newton's third law of motion -- every action has an equal and opposite reaction -- the total momentum of a system is conserved. I can't really think of a way of describing this properly in terms of the question you asked, so I'll leave that to someone else.

3. Nov 8, 2009

### flatmaster

You're basically correct. You need to think of momentum as a vector quantity. Immagine two trains with the same mass and magnitude of velocity collide head-on. The initial Kenitic energy was huge, but actually, momentum was zero!!

p = p1 + p2 = mv -mv = 0

This is why it's important to remember that momentum is a vector quantity. The sign for momentum is going to depend on how you choose your corrdinate system. For my example above, train number 2 was traveling in the negative direction.

4. Nov 8, 2009

### Jeff5738

Thanks. All sorted out.