Newton’s Second Law of Motion gives us the famous equation \(F = ma\text{.}\) The \(F\) on the left side of the equation is the net force, which is the sum of all of the forces that are acting on the object. The \(a\) on the right side of the equation is the acceleration vector, which tells us how the velocity is changing, which in turn can tell us how the position of the object is changing. This equation represents all of the interactions that we can observe, whether it’s ropes, springs, magnets, gravity, or something else.

An important concept that is related to Newton’s Second Law of Motion is momentum. Mathematically, momentum is calculated using the formula \(p = mv\) (where \(p\) and \(v\) are both vectors). Conceptually, momentum can be interpreted the quantity created when there is a mass that is in motion. However, it is difficult to interpret exactly what this quantity is. One interpretation of it is that it’s a measure of how hard it would be to bring an object to rest. Objects with more momentum require more "effort" to make it stop than objects with less momentum. This does not fully capture all of the nuances of momentum, but it’s close enough for us.

We can view Newton’s Second Law of Motion through the lens of momentum. Instead of thinking about the acceleration of an object, we can think about how its momentum is changing. A net force applied for a period of time will lead to a change of that object’s momentum, and that force applied over a time is called an impulse.

Momentum is a deep enough topic that it will be given its own section.