6.1: Newton's second law
Almost all motion and dynamics you see around you can be derived from Newton’s second law and the characteristics of the four fundamental forces of nature. It is amazing that so many phenomena in our daily life can be described by such a deceptively simple equation. There are several reasons for this. First of all, Newton’s laws are not as simple as they seem, and require careful use of vectors, mathematics and kinematic techniques. Secondly, the force term can have many different appearances, leading to a wide variety of motion, and thirdly, most importantly, dynamics can become very complex and difficult to predict when many point masses are present.
Let us have a closer look at Newton’s second law, Equation 4.2:
\[\sum_{j} \overrightarrow{\boldsymbol{F}}_{i j}=m_{i} \overrightarrow{\boldsymbol{a}}_{i} \tag{6.1} \label{6.1}\]
We know from the previous chapter how to interpret the acceleration vector \(\overrightarrow{\boldsymbol{a}}_{i}\), however what is the precise meaning of the scalar mass \(m_{i}\) and the force vectors \(\overrightarrow{\boldsymbol{F}}_{i j}\) ?