# Momentum and Kinetic energy

1. May 10, 2010

### gdpudasaini

Hi everybody! I was thinking about the difference between Kinetic energy and momentum of a body. According to Newton; Momentum is the quantity of motion i.e. momentum is the measure of motion. And Kinetic energy is the energy of motion of a moving body....Now i am confused; The above two definations of momentum and kinetic energy seems to say same thing. Then what is the difference between Kinetic energy and momentum of a moving body? Please can anybody explain me....

2. May 10, 2010

It's best to look at the "mathematical" definitions of momentum and kinetic energy to see the difference. And btw, the "quantity of motion" is definitely not the same thing as the "energy of motion".

3. May 10, 2010

### Staff: Mentor

The biggest difference is that momentum is a vector with units of ML/T and kinetic energy is a scalar with units of ML²/T².

4. May 11, 2010

### gdpudasaini

Its very easy to understand the difference if we look at mathematical equations. But what i want here is the way to visulaize them in a conceptual way..

5. May 12, 2010

### Acut

In short, kinetic energy may be transformed into some other type of energy (electrical, potential...).
Momentum can't be transformed in anything else.

This means that an isolated system always conserves momentum (if you plot momentum versus time it will be a constant), but may or may not conserve kinetic energy (the plot kinetic energy versus time can be anything (of course, always a non-negative value, but besides that, there's no other restriction)).

I'm NOT saying energy isn't conserved. If you plot TOTAL energy (kinetic + potential + whatever other type of energy) of an isolated system, it will always be a constant, if you neglect any relativistic stuff (in which energy may be converted to mass and vice-versa, but if you include it in the "whatever" part, you get your energy conservation back).

Another important diff: momentum is a vector. It has x, y, z components, may be coordinate transformed, you may do vector products with it. Energy is a positive scalar, no components.

The time derivative of momentum is Force (Force is always a vector). The time derivative of energy will give you the power of a system (power is always a scalar).

6. May 13, 2010

### GRDixon

Momentum, like energy, has many forms in nature. As for the difference between the two, a specific example may be instructive. A spherical shell of charge, which has always moved at a constant, low (<<c) speed, has an electromagnetic field characterized by both momentum and energy densities. If the momentum density is integrated over all of space, one obtains a vector result that equals a constant (the shell's "electromagnetic mass") times the shell's velocity. If the magnetic field energy is integrated over all of space, one obtains a scalar result equal to the electromagnetic mass times v*v/2. The field momentum equals part of the force, required to accelerate the charge from rest, multiplied by the time the force acts. (The other part is found in a radiation field). The energy (in the magnetic field) equals part of the force, required to accelerate the charge from rest, multiplied by the distance through which the force acts. These two quantities, while related, have their own particular units and are distinct for this reason, plus the fact that the momentum is a vector quantity, whereas the energy is a scalar. The unit of energy is the joule. It's high time someone gave the unit of momentum a name.