This is not a comprehensive treatment of some complex ideas, but here are some thoughts from today.
I bought myself a copy of Greg Jacob‘s 5 steps to a five to add to our library for pre-service physics teacher. In reading it, I’ve come across a statement that is representative of ontological differences in how physicists think about a few concepts in introductory physics, which I think stems from differences in how one can interpret the equal sign. I don’t have the exact quite, but Greg I think in the text implies that Impulse is both the change in momentum and the product of Net Force and its corresponding time interval.
Impulse = Fnet.Δt = Δp
From this perspective, the equal sign allows one to say that all three things are equally, both quantitatively and ontologically. Impulse is a word for both things.
My thinking about this mathematically is more like
Impulse ≡ F.Δt We’ll define impulse for a single force to be the product or integral.
Then we we can add up individual impulses, to get the Net impulse ≡ Σ Impulses = Σ F.Δt = Fnet.Δt
By applying Newton’s 2nd law, you get that Fnet.Δt = Δp.
Thus Net Impulse = Δp
To me, impulses are causal influences that together cause a change in a momentum, which is the effect. So to me, impulse is not change in momentum, not ontologically, because one is the cause and the other is the effect. So, I guess I see two differences, and they may or may not be related. First, I think we can define impulses for individual forces (and I’m not sure what Greg would think), and I also think that impulses are events whereas change in momentum is a change in state. Since I think they are ontologically different, I would never want to say that impulse is a change in momentum.
Of course, you can take such a momentum perspectives even further, such that even static situations involve momentum flow. In this case, individual impulses each actually flow momentum, such that the net momentum flow is zero. That is, in this perspective, it’s taken even further that each impulse (cause) has an effect (momentum) flow and the momentum flows combined to create a net momentum flow. In other words, the mathematical steps above are different, because Newton’s 2nd law is applied first and then the sum is taken.
And of course, similar differences in conceptualizations exist when we think about work, net work, change in kinetic energy, and the product of Force and displacement.
I’m not necessarily convinced that any way of thinking about this is “correct”, but I do think it’s useful to be able to acknowledge and attempt to reconcile the different ways of thinking about it.
People who I suspect will have an opinion on this: Leslie Atkins, Andy Rundquist, Benedikt Harrer, and many others.