In classical mechanics, the momentum of a particle is the product of its mass and its velocity. As velocity is a vector quantity, so momentum itself is also a vector (i.e. it has both magnitude and direction). In Physics, momentum is usually given the symbol p, made bold to indicate a vector, so:
p = m . v
In words, you could say that something with momentum is a mass in motion – it is going to take some effort to stop that mass, hence why teams or ideas said to have “momentum behind them” are considered to be doing very well and hard to stop.
It is important to note that in this article it is technically linear momentum which is being discussed; angular momentum is a different quantity altogether which relates to objects which are rotating; linear momentum concerns objects which are moving (more or less) in straight lines. Most importantly, linear momentum is a vector while angular momentum is not (angular momentum is actually a type of quantity known as a pseudovector, but that is of no concern in this article).
Each time the word “momentum” is used in this article, take it to mean “linear momentum.”
Conservation of Momentum
Momentum is a conserved quantity, meaning that in any system which is not being affected by outside sources the total momentum will never change. This fact applies throughout all physics, not just classical mechanics, so is very important to remember. It is also related, and was originally expressed, in Newton's First Law:Any object which is in a state of uniform motion will remain in this state unless a force is applied to it.
This is most commonly demonstrated using a device called Newton's Cradle, as shown in the picture attached to this article. The momentum of the end ball is transmitted through the other balls to the opposite end ball, which swings outwards and then back in, transferring the momentum back in the opposing direction. This can continue indefinitely as nothing is acting on the balls to remove any of the momentum in the system.
In reality, of course, there are forces acting on the balls (such as air resistance, and frictional forces in the strings) which will cause them to slow down over time, but as a theoretical exercise the Cradle is an ideal example of momentum conservation in action.
This principle forms the basis of a wide variety of calculations; if a moving ball hits a stationary one, we can now work out how fast the stationary ball will start to move. If momentum is conserved perfectly (for example, a moving ball hits a stationary one, then the stationary ball moves and the initially moving ball stops) this is called a perfectly elastic collision. Of course such ideal situations rarely occur (what if the balls are made of a squishy material, which gives a little on the impact) but as long as we know the composition of the impacting objects we can apply a quantity called the coefficient of restitution and still work out the resulting momenta.
Frames of Reference
Momentum is always measured from a specific frame of reference. This may seem overly complex for simple classical problems but it is a very sound habit to get into.
The easiest way to explain how frames of reference work is with an example. Say you are sitting in a train which is travelling along the track. Because you are moving with the train, you would say that from your frame of reference the train carriage around you is in fact stationary, while the countryside appears to be moving around the train. On the other hand, someone standing in a station as the train goes past would say that the countryside is stationary and that the train is moving. Contrary to what common sense might indicate, in fact both points of view are correct from their own frames of reference!
The more traditional example is a ball sitting in a moving glass elevator. If you are outside the elevator the ball has momentum because it is moving as the elevator does. If you are inside the elevator, on the other hand, the ball has no momentum because you and it are moving at the same rate with the elevator. Inside the elevator and outside it are both valid positions; they are different frames of reference.
Suggested Further Reading
On its own momentum is a relatively simply concept, but even in a simple runthrough of core ideas such as this article many other more complex things begin to appear. Interested readers may wish to look up some of the following terms: elastic and inelastic collisions, kinetic energy, coefficient of restitution, centre of mass, closed system, rigidity, reciprocal actions. Newton's Laws are also good to look up as they form the basis of all classical mechanics including momentum.
References
The Physics Classroom's Physics Tutorials on Momentum and its Conservation, found online at www.physicsclassroom.com on 8th July 2010.
