What is momentum? Why is it given a special symbol p? Here is the answer.

 

Newton’s law is force is mass times acceleration, which is written as F = ma.

 

Acceleration is the change in velocity per second. This is written as a = Δv/Δt.

 

Newton’s law becomes:

 

       F = m Δv / Δt.

 

Since m is constant, we can write this as

 

F = Δmv / Δt, or

 

F = Δp / Δt.

 

What this equation states is that force causes something to change. What is this something? Momentum!

 

This is how to think about it. When we apply a force to an object, we are changing something. Things are different when a force is applied. What is different? Answer: the momentum. This is why it has a special name and a special symbol.

 

F is actually the sum of the forces on the object.

 

Delta. Students have a hard time understanding the meaning of Δ, such as in the equation above a = Δv / Δt. I asked a boy how tall he is. He said 5’10”. I asked him how tall he was last year. He said 5’9”. This means he grew one inch in a year, or his change in height

Δh / 1 year = 1”. Then he understood. We have to focus our explanations on them and their bodies.

 

Suppose F were zero, that is, suppose there were no forces on the object. What can you say about p? Please do not say that p is zero! If F = 0, then the above equation states that

Δp = 0, or the change in the momentum is zero. This means that the momentum is constant. The is the law of conservation of momentum.

 

I took out two toy cars, put them on the desk, and moved them towards each other. They bumped and stopped. I asked students what happened to the momentum they had before the collision.

 

“The momentum just disappeared,” one student said.

 

“Impossible,” I replied, “momentum is conserved. It does not disappear!”

 

After a lot of thought, I told them. In one class, some students knew. Momentum is a vector. The momenta of each car points in opposite directions. Before the collision the sum of the momenta was zero, and so remained zero after the collision.