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(Abbreviated p. Momentum is the oomph something has due to having mass that’s in motion. Let’s say you just happen to be standing in the middle of a football field, minding your own business, when you see a football fly over your head. The next thing you know, a linebacker is coming straight at you, charging like a bull. You turn and make a run for it, but too late! The linebacker rams into your poor body, tossing it into the air and throwing it onto the field with a terrible thud.

You have just experienced momentum. The linebacker’s body had it and then, upon ramming your body, too much of its momentum transferred to your body.

Had the linebacker, instead, been lazily strolling down the field and accidentally bumped you, you would never have left the ground. Had he been less massive, let’s say like a kindergartener, again he could never have tossed you into the air. The combination of great mass and high velocity meant that you were a goner.

The equation for momentum of a piece of matter. For objects made of matter, momentum is defined by Newton’s Laws of Motion as mass times velocity. The linebacker, if strolling, would have less velocity. The kindergartener would have less mass. In either case, the momentum would be less than a linebacker hitting you at full speed.

The equation for momentum is written:
p = mv where p stands for momentum. That is, mass times velocity equals momentum.

Why does p stand for momentum? It really stands for impetus, which is from the Latin impellere from im- + pellere. Pellere meant “to push forcefully.” As im- was a prefix meaning “inner,” impellere meant pushing with an inner source of energy. The abbreviation m isn’t available to symbolize momentum because m is used to symbolize mass.

We might ask to understand momentum in a deeper way and ask: why does mass when moved with velocity create push? At this time, we can say only that it’s just the way it is in our universe; it’s just a law of physics.

The equation for momentum of massless particles. What about particles that don’t have mass, can they have momentum? Yes. Photons, for example, have no mass. It might seem like a stream of photons couldn’t possibly push anything, but they can. If you look on the Internet, you’ll find videos with titles like “Watch a powerful laser beam push a piece of foil forward.” Laser beams are no more than a stream of photons, all moving together in a unified manner.

Massless particles like photons all travel, in a vacuum, at the speed of light. They are “born” with this velocity. Their velocity is an inherent property, not gained from anything else. Their momentum derives from this velocity. Einstein discovered that the equation for the momentum of a massless particle is the speed of light divided by the energy of the particle. This is written:

p = E/c. The letter p stands for momentum (see section above); c stands for the speed of light (a constant); and E stands for energy.

The energy of a massless particle depends on its frequency; the higher the frequency, the more the energy. Thus, we can see from the above equation, the higher the frequency, the greater the momentum. As violet light has a higher frequency than red light, a violet laser would have greater momentum than a red laser.

Momentum is conserved. The momentum in an isolated system is conserved. While momentum can be transferred from one item to another, the total of the momentum in the system remains constant. When a linebacker runs into a poor soul on the field, some of the linebacker’s momentum transfers to the poor soul, who as a result, flies into the air. Careful measurement of the momentum with which the poor soul flies and the momentum of the linebacker after the collision, now slightly slowed, would total the momentum of the linebacker before the collision.

Momentum, linear momentum, and angular momentum. Momentum is also called “linear momentum.” They are the same things.

Angular momentum has a different definition. It is the momentum of an object which is spinning on its axis, circling a central object as a planet does, or traveling in some other curved path. At the quantum level, angular momentum is defined on analogy with the behavior of rotating everyday objects. However, the analogy is loose. In the quantum world, angular momentum can refer either to “spin” or to “orbital angular momentum,” neither of which are very similar to the angular momentum of everyday objects.

Angular momentum is also called “rotational momentum” or “moment of momentum.”