Understanding the Difference Between Kinetic Energy and Momentum

[PhysicsKid0123]

How can you tell the difference between kinetic energy and momentum? I know KE is a scalar and momentum is a vector but physically how do they differ? I don't seem to have a full intuitive understanding. I think I do, but I am unsure. I understand the difference quantitatively, KE= (1/2)mv^{2} and P= m\overline{v}, but what good is it to know the these equations if you do not know the underlying concepts and principles? "Plugging and chugging" is not enough for me. If anyone can give a qualitative conceptual explanation that would be great.

P.S. I'm majoring in physics so that is why I feel the need to really understand.

 

[A.T.]

but what good is it to know the these equations if you do not know the underlying concepts and principles?

Energy and momentum were defined such that they are conserved under certain conditions. There is not much more to it.

 

[jtbell]

You might consider the following parallel between KE and momentum, using (for simplicity) an object that has a single constant force acting on it:

Work-energy theorem: the change in an object's KE = the work done by the force = force · distance.

Impulse-momentum theorem: the change an an object's momentum = the impulse delivered by the force = force · time.

 

[timthereaper]

I don't really think you can say that they're physically separate things. You can't have kinetic energy without momentum, and you can't have momentum without kinetic energy. It's really just 2 ways of describing the same thing happening. Kinetic energy and momentum are different types of measurements (vector vs scalar quantities) and they pertain to different conservation laws, but the same physical event is happening.

 

[russ_watters]

...but what good is it to know the these equations if you do not know the underlying concepts and principles? "Plugging and chugging" is not enough for me. If anyone can give a qualitative conceptual explanation that would be great.

P.S. I'm majoring in physics so that is why I feel the need to really understand.

Some guys, 400 years ago, recognized the usefulness of each quantity; recognizing that in some circumstances they are conserved. There really doesn't have to be any deeper "underlying concept" than that.

...how do they differ?

they differ by their equations, units and domains of applicability (situations where each is conserved). It is useful to think about concepts in physics in terms of the math. The math is essentially everything in the descriptions of the concepts.

And the only way I'd typically say "underlying" applies is when you derive them. So you can show relationships between, say, constant speed acceleration and kinetic energy or momentum.

 

[russ_watters]

I don't really think you can say that they're physically separate things. You can't have kinetic energy without momentum, and you can't have momentum without kinetic energy. It's really just 2 ways of describing the same thing happening. Kinetic energy and momentum are different types of measurements (vector vs scalar quantities) and they pertain to different conservation laws, but the same physical event is happening.

What about where a collision where one or the other is conserved? You might dissipate kinetic energy but not momentum.

 

[PhysicsKid0123]

I didn't mean physically separated. I meant how do you distinguish one from the other when you see an object in motion. I've done a lot of research, and I've come to conclude, to give a conceptual explanation that;

1) Momentum is how the motion of an object carries itself. (this thought almost makes me think of momentum as if it's something ethereal lol.) This is what best defines motion at constant mass and velocity. It has direction, velocity, and mass. That is why I say momentum is how it carries it self. Without even one of these variables it wouldn't be able to "carry itself" to any other position.

2) Kinetic energy is the energy a moving object posseses which may have come from some sort of initial external or internal work or force which had it transferred to give it motion. *In a sense* I see kinetic energy like a form potential in energy in motion.

This is the best way I can conceptualize the characteristics of motion with regards to kinetic energy and momentum. What can you say about this? Anything wrong? If so, you're welcome to build up on what I have stated!

 

[A.T.]

Anything wrong?

http://en.wikipedia.org/wiki/Not_even_wrong

 

[timthereaper]

What about where a collision where one or the other is conserved? You might dissipate kinetic energy but not momentum.

Is there a situation where this happens? I thought that to get the value for kinetic energy, you basically sum up the change in momentum dotted with the velocity vector, so a change in one means a change in the other. I could be wrong though.

EDIT: I am wrong. I forgot that in systems momentum is always conserved, but kinetic energy depends on the current velocities of the particles, so it changes.