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--- frameworks:newtonian_formalism [2018/03/29 15:18]
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-====== Newtonian Formalism ======
-<tabbox 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.
-  * **[[equations:newtons_second_law|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.
-<tabbox Concrete>
-The equations and the framework of classical mechanics were deduced historically from experiments. This worked pretty good but is highly unsatisfactory from a theoretical point of view. Newton proposed his [[equations:newtons_second_law|second law]]
-\begin{equation} \label{newtonssecond}  \tag{1} F = m \frac{d²}{dt²}q =m \ddot q,  \end{equation}
-where $m$ is the mass, $\ddot q$ the acceleration and $F$ the force that acts on the object in question.
-To describe some object we simply have to deduce equations for the forces $F$ that act on the object from experiments and put them on the left-hand side of the equation. This yields a differential equation, which we must solve for $q=q(t)$.
-The solution is called the trajectory of the object and describes the position of the object for every moment in time. This is one framework for classical mechanics and it‘s useful for many, many things.
-Every student of physics must solve Newton's second law for many different situations.
-----
-**First law:**
-If the forces acting on an object are balanced, i.e. the total force is zero $\vec F=0$, the velocity of the object will remain constant: $\vec v=\text{const}$. So when the velocity is zero, it will remain zero. If the velocity has some other value it will keep it.
-<diagram>
-||||| AA|| |AA=Forces are balanced $ \vec F=0$
-||||||!@4|||||||
-|||||BB||||||BB=$ \vec a=0$
-||||,@4| -|^|- |.@4 | | | |
-||| AA||BB |AA=Object at rest: $\vec v=0$|BB=Object in motion $ \vec v\neq 0$
-||||!@4||||!@4|||
-||| AA||BB |AA=Object stays at rest: $\vec v=0$|BB=Object remains in motion $ \vec v \neq 0$; same $ \vec v$.
-</diagram>
-**Second law:**
-$$ \vec F = m \vec a$$
-<diagram>
-||||| AA|| |AA=Forces are unbalanced $ \vec F\neq 0$
-||||||!@4|||||||
-|||||BB||||||BB=$ \vec a \neq 0$
-||||,@4| -|^|- |.@4 | | | |
-||| AA||BB |AA=acceleration $\vec a$ depends directly on the net-force $\vec F$ that acts on the object|BB=acceleration $\vec a$ depends inversly on the mass $m$ of the object
-</diagram>
-<tabbox Abstract>
-<note tip>
-The motto in this section is: //the higher the level of abstraction, the better//.
-</note>
-<tabbox 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 [[:frameworks|alternatives]] it is much easier to understand what is going on, since only concepts that are directly familiar to high-school students are used.
-</tabbox>

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