Newton's Laws of motion

Newton's laws of motion describe the way forces interact with objects in motion. The laws were introduced by Isaac Newton for the first time in his book Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) published in 1678. To this day these laws are used to calculate easy and complicated things regarding motion of objects.

Newton's 1st Law

Lex I: "Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare."

Law 1: "A body will remain at rest or remain moving with a constant velocity unless acted upon an external and unbalanced force."

As long as there are no forces acting upon an object or the resultant forces are equal to 0, the velocity of the object will not change.

Example

In this figure the apple hangs on a branch of an apple tree. There is a gravity force applied to the apple and since the apple does not fall, there is also a force from the tree working on the apple to hold the apple in its place with an equal magnitude, but in opposite direction. That means that there is no net force working on the apple and the apple must be in rest or moving with a constant velocity. In this case the apple is in rest.

Newton's 2nd Law

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

Law 2: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

The equation that belongs to the 2nd law of motion is the following.

Where $\Sigma \vec F [N]$ is equal to the resultant force on an object, $m [kg]$ to the mass of an object and $\vec a [\frac{m}{s^2}]$ to the acceleration of the object.

Example

In this figure the apple has started to drop. For the sake of simplicity friction due to air can be ignored. This means that sum of all forces is equal to $F_g$. With the mass of the apple equal to $m$, the acceleration will be equal to $\vec a = \frac{F_g}{m}$. Since the apple tree is placed on planet earth, the acceleration will be equal to $g$ which has a value of $9.81\frac{m}{s^2}$ on earth.

Newton's 3rd Law

Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.

Law 3: To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Example

In this figure the apple has reached the ground. Newton's 3rd law can be applied here. Due to gravity the apple exerts a force $F_g$ onto the ground which is the action. For every action there always is an opposite equal reaction, which is the normal force $F_{normal}$ that the ground exerts onto the apple.