## A More Advanced Look at Newton's LawsA more formal way to look at Newton's laws for the advanced student is as follows:
This helps to define the basic force law, f=ma, where f is the net force acting on the object. You can have many different forces acting on an object, but if they all cancel each other out, then there is no net force and therefore no acceleration. The equation f=ma defines a force as a mass times an acceleration. Note that acceleration can be a change in either speed or direction. Given any two of force, mass, and acceleration, the third can be found. Because acceleration is the first derivative of velocity and the second derivative of position, this equation can be rewritten in terms of those quantities.
Written as an equation, the second law becomes: f=dp/dt where p is the momentum and t is time. This is another way of stating f=ma. Because p=mv and mass does not change, it follows directly. This gives a much more quantifiable method of calculating momentum conservation.
This law, for all its complex repercussions, is as simple as it sounds. There are some specific instances when it does not apply, however. One example of this, although too complex to discuss here, is the force between moving point charges. |