# Momentum is always conserved

1. May 26, 2008

### glueball8

I don't understand how I can be at rest and then start walking or when a ball hits the wall it bounces back while the wall get no momentum at all?

2. May 26, 2008

### Ed Aboud

As far as I know, conservation of energy underlies conservation of momentum, so therefore if a ball hits a wall and bounces back some of its kinetic energy is converted to other forms such as heat and sound which appear in the wall.

3. May 26, 2008

### mathman

In the cases you mentioned there is momentum transfer to the earth (via the wall in the second case). Since you and the ball are a lot less massive than the earth, the velocity effect on the earth is extremely small.

4. May 26, 2008

### aerospaceut10

In either case, momentum is conserved. It's just that the wall is rigidly connected to the ground/Earth and likewise for your walking scenario. Remember that it's mass times velocity to get that momentum figure, so if you have such a large mass, the Earth, it'll have to have an insignificant velocity, essentially, when your tiny mass moves at the given velocity.

5. May 26, 2008

### glueball8

So what about that I can walk from rest? How is the momentum conserved here?

6. May 26, 2008

### Staff: Mentor

As you move forward with momentum +P, the ground/Earth is pushed back with momentum -P. Since the ground/Earth is so massive, you won't notice its backward movement. (As mathman and aerospaceut10 already explained.)

7. May 26, 2008

### Phlogistonian

When you walk, you push against the earth. Theoretically, this gives it a very slight velocity in the opposite direction, but it's too small to be detected.

8. May 26, 2008

### rockerdoctor

here is another way to think about it. think of someone driving a car. the car has momentum. when the car comes to a stop at a stop sign, all the momentum in the car is pushed into the road. this is why you frequently see ripples in the road at places where there are frequent stops. all the momentum must go somehwere so it goes into pushing up the road. momentum is always conserved

9. May 26, 2008

### Cyrus

"Theoretically"?.......... "velocity in the opposite direction?" ..........."To small to be detected"...........? ............

Hint:
$$m_ev_{e,1}+m_pv_{p,1}=m_ev_{e,2}+m_pv_{p,2}$$

Do some algebraic manipulation and get this"

$$v_{1,e}-\frac{m_pv_{p,2}}{M_e}=v_{e,2}$$

Now, how did you deduce the earth moves "in the opposite direction?" Something should have yelled to you, wait a minute, that doesnt make sense by the sound of what I just wrote.

Last edited: May 26, 2008
10. May 26, 2008

### Phlogistonian

The OP phrased the question as starting from rest. Whenever I answer a question, I take the OP's conditions as implicitly given. I'm sorry if this confuses you.

Actually, I'm not sorry. You're just an annoying nitpicker.

And how do you propose to measure the motion of the earth due to a person walking around upon it?

11. May 26, 2008

### Cyrus

The initial velocity of the person was set to zero as part of the algebraic manipulation.

Please explain how the earth goes in the 'opposite direction'.

12. May 26, 2008

### Phlogistonian

Cyrus,

Ah, I see your point now. I didn't see it at first. Your point is still stupid.

I have to specify that the earth is moving before I take a step? Why? What absolute reference frame are you using?

13. May 26, 2008

### Cyrus

As long as you see my point, im happy. Statements like "very slight velocity in the opposite direction" sound very, very wrong.

14. May 26, 2008

### D H

Staff Emeritus
It's not nice to be rude.

Particularly when you are wrong.

15. May 27, 2008

### Loren Booda

If (for an elastic collision) momentum of a ball incident upon a wall is equal and opposite to its resultant momentum, would it be correct to assert that the mass and rigidity of the wall approach infinity?

16. May 27, 2008

### Cyrus

Ok, sorry if I was rude.

DH, I read what they wrote. They were using a reference frame of the earth being stationary, I did not. In the case where its not stationary, the earth does NOT move backwards.

I just showed this using the simple conservation of momentum equation. I have no problems with you stating im wrong, but then show me where my equation is incorrect.

17. May 27, 2008

### D H

Staff Emeritus
Conservation of energy, linear momentum, and angular momentum are three distinct concepts. Suppose you take a drive in your car down the freeway, and wham, your car instantaneous reverses its velocity vector, throwing you against the steering column at 120 mph. The car's speed is 60 mph before and after the velocity reversal, so kinetic energy is conserved. Fortunately, that never happens because of conservation of momentum.

The three conservation laws are related through Noether's theorem. Some quantity is conserved for a system in which the Lagrangian exhibits a symmetry. Energy is conserved if the Lagrangian is temporally symmetric. Linear momentum is conserved if the Lagrangian is symmetric with respect to position. Angular momentum is conserved if the Lagrangian is rotationally symmetric.

18. May 27, 2008

### Staff: Mentor

What's your point? You seem to relish giving out more heat than light.

Of course, the Earth "moving backwards" is from the initial inertial frame in which everything started at rest. Duh! You do understand the concept of velocity and reference frames, don't you?

19. May 27, 2008

### Cyrus

Ok, but it wasnt clear to me at all that was the reference frame you were using, so when I read the earth 'moves backwards an undetectable amount', I said to myself 'what the heck!, I dont think so!', thus my frustration.

My apologies, all.

20. May 27, 2008

### rewebster

If you were standing still on some marbles, and then decided to start walking forward---what would happen to the marbles you were standing on?