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Newtonian Formalism
Intuitive
The Newtonian formalism is a framework that allows us to predict how a system will evolve.
The basis of it is summarized by three laws, commonly called "Newton's laws of motion":
- First law: No force is needed to keep an object moving. If an object is at rest, it will remain at rest unless a force acts on it. Similarly, if an object moves with some constant velocity, it will keep moving unless a force acts on it.
- Second law: The way the movement of an object changes depends only on two things: its mass and the total force acting on it.
- Third law: Whenever an object exerts a force on another object, inevitably this second object will also exert a force of equal magnitude on the first object.
Concrete
First law:
If the forces acting on an object are balanced, i.e. the total force is zero $F=0$, the velocity of the object will remain constant: $v=\text{const}$.
| Forces are balanced $ \vec F=0$ | ||||||||||||||||||||||||
| $ \vec a=0$ | ||||||||||||||||||||||||
| Object at rest: $\vec v=0$ | Object in motion $ \vec v\neq 0$ | |||||||||||||||||||||||
| Object stays at rest: $\vec v=0$ | Object remains in motion $ \vec v \neq 0$; same $ \vec v$. | |||||||||||||||||||||||
Second law:
$$ \vec F = m \vec a$$
| Forces are unbalanced $ \vec F\neq 0$ | ||||||||||||||||||||||||
| $ \vec a \neq 0$ | ||||||||||||||||||||||||
| acceleration $\vec a$ depends directly on the net-force $\vec F$ | acceleration $\vec a$ depends inversly on mass $m$ | |||||||||||||||||||||||
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
The Newtonian formalism is still one of the most popular ways to describe what happens in a physical system. In contrast to the alternatives it is much easier to understand what is going on, since only concepts that are directly familiar to high-school students are used.
frameworks/newtonian_formalism.1522128285.txt.gz ยท Last modified: 2018/03/27 05:24 (external edit)
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