Intuitive

Newton's second law tells us that how an object $\color{magenta}{\text{gets faster}}$ depends on its $\color{olive}{\text{mass}}$ and the $\color{blue}{\text{total force }}$ acting on it.

Formulated a bit differently it tells us that the $\color{magenta}{\text{acceleration}}$ of an object is given by the ratio of the $\color{blue}{\text{force }}$ acting on it divided by its $\color{olive}{\text{mass}}$.

However, take note that it is not sufficient to describe a physical system. Additionally, to describe a system we need to know what forces act on the object and what equations describe them. Famous examples of such force laws are

• Newton's law of gravity
• Lorentz' force law
• Coulomb's force law

So, for example, when we want to describe the movement of a planet around the sun we need to think about what forces act on the plant. For this system gravity is the most important force since both objects - the sun and the planet - a superheavy. Therefore, to calculate the movement of the planet, all we have to do is use Newton's law of gravity to calculate the force acting on it. Then, when we have calculated the force we can use Newton's second law to calculate the acceleration of the object. Then, given some starting point and starting velocity of the planet we can calculate where the planet will be at every point in time in the future.

Concrete

Abstract

Why is it interesting?

Newton's second law is the most fundamental equation of classical mechanics. It is still used nowadays, for example, by engineers.

Definitions

• $\vec F$ is the force that acts on the object in question.
• $\vec a$ is the acceleration of the object. The acceleration is the rate of change of the velocity $\vec v$ of the object, which in turn is the rate of change of the location $\vec r$ of the object: $a = \ddot{r} = \dot{v}$.