**Momentum**

Momentum is one of those concepts that can really be placed into any unit in physics. Like energy, its everywhere and must be conserved. As a matter of fact, another of the big conservation laws in physics is the Law of Conservation of Momentum, which states that when no external forces are acting on a system of objects, the total vector momentum of the system remains constant.

If you are hit by a feather that is flying through the air at 75 km/hr (and it does not hit your eye!), you might not even notice it. If you are standing right next to and leaning on an 18-wheeler, it will not hurt you. But put those two things together if the 18-wheeler is running down the highway at 75 km/hr and hits you splat!

**It is not the velocity that hurts you; it is not the mass that hurts you; it is the combination of the mass and velocity. That is momentum.**

Momentum is the product of the mass times the velocity of an object. The symbol for momentum is p.

If 2 football helmets (or any other 2 objects) move toward each other on the same path, they will collide. When they collide, what will happen?

They will each rebound backwards. This happens because momentum must be conserved. And since momentum is a product of the velocity of an object, it, like velocity, is a vector quantity so it has direction.

Another way to state the **Law of Conservation of Momentum** is to say that the total momentum of a system of objects before a collision is equal to the total momentum of the system of objects after a collision (assuming no outside forces act on the system).

So **momentum before = momentum after**

before [m_{R}v_{R} + m_{B}v_{B}] = after [m_{R}v_{R} + m_{B}v_{B}]

(NOTE: R = red helmet; B = blue helmet)

If one direction is positive, the other is negative.

Then you substitute in known values and solve for any unknowns.

A change in momentum is called **impulse**.

Starting with p = mv

And substituting a for v/t into Newtons 2^{nd} law formula (F = ma)

F=m (v/t)

F x t = m x v

F x t is the impulse, therefore

Impulse = the change in momentum

**Impulse = force X time interval**

An impulse is equal to a force times the time interval during which it acts.

This also holds true for rotational motions. **The Law of Conservation of Angular Momentum** states that the angular momentum of an object is unchanged unless a net external torque acts on it. Examples of this are a rotating flywheel, an ice skater (ever seen one spinning?), or a man sitting on a rotating stool holding a tire on an axle.

The angular impulse of a rotating object is equal to the change in angular momentum.

**torque X change in time = change in angular momentum**

Angular momentum of rotating objects is related to the distribution of mass of the object. If the distribution of mass is changed (such as the figure skater who holds her arms out or in), then the angular velocity of the object must change in order to keep the angular momentum constant.

The Impluse-Momentum theorem uses two concepts and sets them equal to each other.

**F /\t = m/\v**

Where F x t = Impulse

Impulse = the change in momentum

This concept can be used to conceptually explain many impacts that occur every day. For example, when you want o hit a homerun in baseball, you will be told to “swing through”. You can’t do anything about the mass of the ball or how much force you can apply, but you can change the contact time. Increasing this time on the left side of the equation will increase the change in velocity on the right side of the equation, therefore giving you a greater distance from the impact.

Crumple zones on cars also use this theorem. When you are traveling at 60 mph down the road and unfortunately run into a tree, you can’t do anything about the speed – you are coming to a stop (change in v), nor can you change the mass. But you change the contact time with the tree by having a crumple zone on the car. This in turn will decrease the force applied to the tree (and consequently, the car). This concept also applies to the air bag safety device.

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