### Momentum, Conservation of Momentum, and Impulse

I remember hearing this word a lot while growing up, but never quite understood what it really meant until much later. People tend to associate momentum with velocity, or speed. Take a person riding a bicycle approaching a downhill stretch. If the stretch of downhill becomes an uphill after say, 100 meters, you might conclude that he should work up as much “momentum” as possible on the downhill to make it easier to climb the uphill.

Naturally, a child might deduce that momentum simply means speed. Well, not exactly. Momentum in classical mechanics, is the product of the mass and velocity of an object. This means that it’s not only the velocity of the object but the weight of the object as well! Looking at it this way, a bowling ball is obviously going to have more momentum than a ping-pong ball, both traveling at equal velocity.

So to use the bicycle analogy, an 80 kilogram rider will have more momentum than a 50 kilogram rider traveling at the same speed and using the same bicycle. Of course, this does not take into consideration the effects of wind drag, which is the force of the wind pushing against you countering your momentum. But unless the 80 kilo guy has a parachute attached to his back, wind drag is probably negligible for this example. Oh, and the 50 kilo guy’s not allowed to have a jet-pack or thruster of any kind 😉 .

So momentum is not only the speed, but the driving force or power behind the object at the given speed. You can remember the equation as p=mv, or momentum(p) is equal to mass(m) times velocity(v).

A related quantity is “impulse”. Impulse is denoted J and is the force acting on an object over a given period of time, J=FΔt. All moving objects have momentum, but how do objects begin moving in the first place? Some force has to “act” on it, or cause it to move. This is what impulse is. Impulse is simply the change in momentum, or force (mass times acceleration) times the change in time – 80 kilograms times his rate of acceleration over the period of time he’s accelerating!

Conservation of Momentum and the Acceleration due to Gravity

This law states that “the total momentum of any group of objects remains the same unless outside forces act on the objects.” Basically, what it’s saying is that unless there’s a disturbance of some kind, all objects that have any kind of momentum will conserve that momentum indefinitely. So does that mean if you were to throw a rock up in the sky, it will keep climbing?? Well, in short, yes! That is of course, only if the forces of gravity and air resistance were not present.

The force of gravity is in this case also known as the weight of the object, and is denoted as FW=mg. FW is the weight force, and is the product of the mass of the object and the acceleration due to gravity – 9.8 meters per second per second (g). This weight force or force of gravity is ever-present in our lives here on Earth and is what keeps that rock from climbing straight out into outer space.

Air resistance, also known as drag, is the force that planes must overcome in order to fly and is also what skydivers use in their favor to prolong their descent toward the Earth’s surface. The law of the conservation of momentum is what Newton’s first and third laws of motion are talking about, the law of inertia and the law of reciprocal actions. These are:

“Every body continues in its state of rest or of uniform speed in a straight line unless it is compelled to change that state by forces acting on it.”

And,

“Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.”

Both the law of inertia and the law of reciprocal action come about due to the same conservation of momentum! Due to these laws, one can calculate and understand the movement of various bodies and where they will go when there are collisions or even explosions. Billiard balls display this law extensively making it a perfect example. The cueball collides with another ball and transfers its momentum partly or completely, while losing some to friction and gravity as well.

In the end, the original force with which the cueball was struck with, is divided arbitrarily between it, the second ball, and “outside forces” such as friction and gravity. How it’s divided depends mainly on the path of collision and the coefficients of air, sliding, and rolling friction between the balls and the table.