# I Force and rate of change of momentum

1. Feb 24, 2016

### alkaspeltzar

My question is simply..if force does equate to the rate of change of momentum, then why is it not taughted as this rate rather simply a push or pull?

Is it becuase really they are the same thing and it is much easy to explain/work with? Just curious

Guess up until now I didn't even think of force as a rate of change of momentum...maybe I'm old school

Thanks

2. Feb 24, 2016

### Staff: Mentor

Force is still push or pull. Only NET force (vector sum of pushes and pulls) is rate of change of momentum.

3. Feb 24, 2016

### alkaspeltzar

Okay, so it is only the NET force which can be considered equal to the rate of change of momentum. Got it!

Is it probably because in most applications(or at least what I work with in school and engineering) we only worry about the simple forces that then this relationship doesn't apply, so force is simply the push pull and we leave the rate of change of momentum out of it?

I do understand the relationship between force and momentum now.....I guess what is bothering me is that for years, I have been able to think and do my calcs and never needed to use the relationship until now. Guess it has me confused if I should be thinking of force differently than classic F=ma, push pull that has been drilled into my head.

Thank you

4. Feb 24, 2016

### Staff: Mentor

You can, of course, leave out ma if it is a static equilibrium problem. But, in dynamic situations, ma needs to be included.

5. Feb 24, 2016

### A.T.

An individual force is the rate of momentum transfer.
Net force is the rate of total momentum change.

The F in F=ma stands for net force, which is the rate of total momentum change.

6. Feb 24, 2016

### alkaspeltzar

Okay but my main question is a physical force the same as a rate of change in momentum? Like if I hit a wall with a force is that the same as saying I hit the wall with a rate of change of momentum?

Or is simply rate of change of momentum related to force therefore we can calculate with one or the other?

7. Feb 24, 2016

### Staff: Mentor

A push force or a pull force is sometimes (infrequently) referred to as a rate of momentum transfer. But you can't represent it as mass times acceleration unless it the only (net) force acting.

8. Feb 24, 2016

### HallsofIvy

"Force equals the rate of change of momentum" means that $F= \frac{d(mv)}{dt}$. In the special (but important) case that mass, m, is constant, that is the same as $F= m\frac{dv}{dt}= ma$.

9. Feb 25, 2016

### A.T.

10. Feb 25, 2016

### alkaspeltzar

Sorry bear with me but I am just not getting it.

So are you saying that the physical force(what we long ago defined as a push or pull) is exactly the same as rate of change in momentum, aka the rate of momentum transfer?

Don't you have to have a force to have a rate of change in momentum? Part of me thinks if a body has acceleration, then there must be a force. Likewise, if a body has a rate of change in momentum, it must have a force causing it.....so aren't they two separate things, just related since one cant exist without the other?

And if they are the same, why don't we use one name....why say force if it is really a rate of momentum transfer or visa versa?

I guess I m looking for a simple explanation, please no math at this point.

11. Feb 25, 2016

### Staff: Mentor

Historically, using terms like "rate of momentum transfer" to represent a contact force (push or pull) came about when people began realizing the analogy between the differential equations for the force balances in continua, and the differential equations for heat- and mass transfer. In these sets of equations, the forces per unit area appear in the same locations in the equations as the rate of heat flow per unit area and the rate of mass flow per unit area. So, it became natural for them to start referring to the force per unit area as the rate of momentum flow per unit area (or the rate of momentum transfer per unit area).

12. Feb 25, 2016

### alkaspeltzar

that is not helping me, I am sorry that is more advanced than I can understand. Can you or someone please explain what I have asked above? I just want to know if really, they are the same thing, regardless of name or the math. Looking to have someone explain how a rate of change in momentum really is a contact force

13. Feb 25, 2016

### A.T.

Change and transfer are not the same. Change is the sum of all transfers: the net effect.

For the same reason we use the word "velocity" instead of "rate of position change".

14. Feb 25, 2016

### Staff: Mentor

In the normal context of applying physics at the level you are asking about, I would never refer to an individual force as a rate of change of momentum, unless it was the only force acting on a body, in which case it would also then be equal to the rate of change of momentum of the body. But, if there are multiple forces acting on a body, I would only consider the resultant of these multiple forces (i.e., the net force) as being equal to the rate of change of momentum of the body, and I would not consider each one individually as being the same thing as a rate of change of momentum.

Now this may differ from how A.T. looks at it, but that is just a matter of personal taste and preference.

15. Feb 25, 2016

### alkaspeltzar

A.T., so are you saying that rate of change of momentum is not the same as rate of momentum transfer?

Assuming net forces; "Force equals the rate of change of momentum" means that F=d(mv)dt' , does that mean the FORCE IS PHYSICALLY the rate of change of momentum or is this just a math relation?

16. Feb 25, 2016

### alkaspeltzar

So Chestermiller, what you are saying is that yes, the force and rate of change of momentum are the same, assuming it is the only force(or total net force)?

Doesn't the force CAUSE the rate of change of momentum, so they are different entities still?

17. Feb 25, 2016

### Staff: Mentor

That's how I view it.
I would agree with this interpretation also.

18. Feb 25, 2016

### A.T.

What is the difference and why should we care?

Since both happens simultaneously, how would you know which is the cause and why should we care?

19. Feb 25, 2016

### alkaspeltzar

If they are different entities though, wont they have different units? Unit for rate of change of momentum are same as force, how come?

20. Feb 25, 2016

### alkaspeltzar

Well since highschool, college and now engineering, force has always been a push or a pull, calculated by F=Ma, with the understanding that a change in acceleration or momentum is cuased by a force. Hearing a force said it is a rate of change of momentum seems foreign and is outside my understanding, so I am asking trying to understand how or why it is or isn't the same thing.