Momentum and Impulse

Sir Isaac Newton described momentum as "a quantity of motion". Although in class we state Newton's Second law in the popular form (F=ma), he might have though it more appropriate to refer to it as a force causing change in the momentum of an object. We'll take a look at several different ways to approach this problem.

First, let's start by defining momentum (p) as the quantity mass time velocity, or p=mv. This is a vector quantity (the direction that our momentum is being applied in is very important) and the units are kg-m/s, or the Newton-Second.

Impulse is defined as "a change in momentum". We can write this as Dp, or p - po. Anytime we look at a change in something, we will be looking at the final quantity minus the initial quantity. Again, it is important to keep our signs (direction) straight! Impulse may also be the result of applying a force on an object for a specified period of time. Mathematically, we would say that impulse equals Force times time, or F t. So: Impulse = Dp, or Impulse = Ft. We'll combine these and say:

or

Another idea to discuss is that of "mass flow rate". Mass flow rate is the rate that mass is moving (or changing), measured in kg/sec. When we multiply this by the velocity the mass is moving, we also get the force applied by the moving mass stream. Hold that thought.

Momentum is conserved. OK - not a new concept - we have previously discussed this in Physics. This means that, in an isolated system, the total momentum in the system remains constant, or the momentum before an event is equal to the momentum after an event. How does this apply to our study of rockets? There is a popular misconception that the reason a rocket moves is that the exhaust gases push against the ground or the atmosphere and cause the rocket to be propelled forward. In fact, a rocket is able to move through the vacuum of
space where there is nothing for the gases to push against. What's up with this? The answer is an application of Newton's Third Law and the principle of Conservation of Momentum. I think either explanation is valid. The hot gases from the propulsion system are expelled from the rocket with a great deal of force (equal to the mass flow rate times the velocity of the gases). The reaction pair is the gases pushing the rocket in the opposite direction but with an equal magnitude of force. We can use Conservation of Momentum to help determine the velocity a rocket will have. The force applied to the rocket by the expelled gases is the mass flow rate times the velocity of the gases. Applied for a given amount of time, this equals the momentum of the gases. The momentum of the gases must equal the momentum of the rocket, but in the opposite direction since these must add to equal zero (the momentum of the system before ignition.)