# Momentum is always conserved

## Main Question or Discussion Point

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?

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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.

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.

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?

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.

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

Doc Al
Mentor
So what about that I can walk from rest? How is the momentum conserved here?
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.)

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.

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

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.
"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.

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"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.
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?

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'.

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?

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

D H
Staff Emeritus
"Theoretically"?.......... "velocity in the opposite direction?" ..........."To small to be detected"...........? ............ It's not nice to be rude.

Particularly when you are wrong.

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.)
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.
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.

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?

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.

D H
Staff Emeritus
As far as I know, conservation of energy underlies conservation of momentum
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.

Doc Al
Mentor
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.
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?

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?
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.

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