# What is the difference between Kinetic Energy and Momentum?

1. Sep 10, 2011

### Acid92

I know what they are Mathematically and their definitions but looking at them from an intuitive way as a property of physical objects, I cant seem to distinguish them

Ive always understood kinetic energy intuitively as an objects intrinsic ability to exert a force over some distance by virtue of it moving and obviously as an object gets heavier or faster this ability increases (We can easily instantiate this example intuitively with colliding objects etc) but then we can look at momentum from this point of view aswell

So from an intuitive perspective with respect to the two concepts as properties of objects, what really is the difference between the two?

2. Sep 11, 2011

### Drakkith

Staff Emeritus
See here: http://www.batesville.k12.in.us/physics/phynet/mechanics/energy/KENOTMomentum.html

Also, see here: http://www.newton.dep.anl.gov/askasci/phy05/phy05039.htm

What I get from all this is that KE is how much energy something possesses, while momentum is not.
It looks like momentum is a vector quantity while kinetic energy is not. One thing stated is:
For example, the Earth in orbit around the Sun can be approximated to have near zero change in kinetic energy, but it is constantly changing its momentum.

I'm not really sure if either of these are "properties" of objects.

Last edited: Sep 11, 2011
3. Sep 11, 2011

### Ken G

And even for just one-dimensional motion, there are important differences. Momentum is basically what you get when you apply a force over a time, and energy is what you get when you apply a force over a distance. The difference is very sensitive to the mass (inertia) of the object, because you can supply a force over a time, but if you are dealing with a large mass it might take a long time before you get much velocity. Without much velocity, you can apply a force for a very long time without the object covering much distance (that's why kinetic energy has an extra power of velocity in its definition). So it's easier to impart momentum into a massive object than it is to impart energy into it. Low-mass objects are just the opposite-- a force for even a short time will generate a large velocity and lots of energy, even if the momentum is not particularly high. (A good example of that is the sunlight that can make you feel very hot without your feeling any "push".)

Last edited: Sep 11, 2011
4. Sep 11, 2011

### klimatos

The dimensions of momentum are ML/T. It is measured in kilogram-meters per second. It is a vector quantity, having both direction and magnitude.

The "cousin" of momentum is force or impulse, with which it is often confused. The dimensions of impulse are ML/T^2 and it is measured in Newtons. Impulse is momentum over time. It is a vector quantity, have both magnitude and direction.

The dimensions of kinetic energy are the same as for all energy, ML^2/T^2. It is measured in Joules. It is also a vector quantity, having both direction and magnitude.

A gas molecule traveling through space has both momentum and kinetic energy of translation. It may or may not have internal energies of rotation and/or vibration/libration.

When that molecule impacts upon a surface, an impulse is generated.

5. Sep 11, 2011

### klimatos

1. Not so. Your dimensions are off. Momentum has the dimension of ML/T. Force (ML/T^2) over time has the dimension of ML/T^3. I don't know what that might be, but it is not momentum.

2. True.

3. Not true. Energy has the dimension of ML^2/T^2 and is measured in Joules. Sunlight has the dimensions of (ML^2/T^3)/L^2 or M/T^3 and is measured in watts per square meter. It is power (not energy) over area.

Sunlight may or may not make you "feel very hot". The temperatures that we "feel" are factors of a large number of physiological, psychological, and meteorological conditions.

6. Sep 11, 2011

### Staff: Mentor

In colloquial English, "apply a force over a time" does not mean "divide force by time," but rather, "apply a force for a time [interval]" or "apply a force during a time [interval]."

(force) x (time) is called "impulse" and has dimension ML/T, the same as momentum. In fact the impulse delivered by a (net) force that acts on an object during a time interval equals the change in momentum of the object during that time interval. This is the "impulse-momentum theorem". It's analogous to the "work-(kinetic) energy theorem" which says that the work (force x distance) done on an object by a (net) force equals the change in the object's kinetic energy.

7. Sep 11, 2011

### Ken G

Yes, I meant jtbell's interpretation. Impulse and force are not the same thing-- impulse is a change in momentum, so is intimately related with momentum, not with force alone. I stand by everything I said, including the fact that sunlight makes us warm without pushing on us is a classic example of why energy tends to be more important than momentum for low-mass objects (and photons are of course the ultimate low-mass object). The fact that when we treat the Earth as immovable, as we often do in physics problems on Earth, it often means that energy will be conserved in those problems but not momentum (like hitting a tennis ball against a wall), is a classic example of how momentum tends to be more important than energy for very massive objects (like the Earth). These are important considerations for understanding the physical differences between momentum and energy.

Last edited: Sep 11, 2011
8. Sep 12, 2011

### A.T.

KE and momentum are both frame dependent, so they are not intrinsic properties of an object. Just some quantities assigned to the object by the reference frame.

9. Sep 12, 2011

### A.T.

Impulse is to momentum like work to kinetic energy. And force is not the same as impulse.

Last edited: Sep 12, 2011
10. Sep 12, 2011

### A.T.

The main useful thing about those concepts is their conservation laws. And here also lies the crucial difference:
- Momentum of an isolated system is always conserved.
- Kinetic energy of an isolated system is not always conserved, just the total energy. You can change the KE of the system by converting it in/from other energy types.

11. Sep 12, 2011

### sweet springs

Hi, Acid92

Let us think of two particles have same mass, same magnitude of velocity but opposite direction. Momentum of the system is zero, however, kinetic energy of system is positive value which is the double of one.

Momentum is additive vector and energy is additive value. Or in relativistic theory, (Energy, Momentum x, Momentum y, Momentum z) forms "4-vector" though energy here is not only kinetic energy but whole energy including rest mass energy.

Regards

Last edited: Sep 12, 2011
12. Sep 12, 2011

### chrisbaird

The best way to understand the difference is to get a feel for the difference of the conservation laws. Set up on paper a one-dimensional collision event (two train cars on a frictionless track with different initial velocities collide) and apply the conservation of energy and the conservation of momentum to solve the system, and you will get a feel for the differences. For instance, if the cars have equal mass and equal and opposite initial velocities, the total initial momentum is zero, but the total kinetic energy is not.

13. Sep 12, 2011

### klimatos

I stand corrected and apologize to all. Impulse is not simply force but force applied over time. This is dimensionally equivalent to the change in momentum. I do know better, but apparently had a brain lapse while posting. (grovel)

14. Sep 12, 2011

### Ken G

It was a good clarification-- force "over" a time can certainly sound like a division rather than the intended multiplication.