Newton Laws

Summary

Newton's laws are descriptions of forces best described in a perfect vacuum and in inertial frames of reference.

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⏱ 1 min

Definition

Newton's laws are a set of experimentally proven results that describe classical forces.

Newton's first law is "an object will continue in their motion unless a force acts on it." Which is true because in an inertial frame of reference, if an object is moving at some velocity in a vacuum space, it will continue with the velocity unless acted on by a force.

Newton's second law is "The amount of force on an object can be described as $F = m a$ ."
This is a mathematical statement to describe the force an object has in relation to its mass and acceleration.

Derivation of Newton's Second Law through linear momentum

$\begin{matrix} p = m v \\ \frac{d p}{d t} = m \frac{d v}{d t} \\ \underset{F}{\underset{⏟}{\frac{d p}{d t}}} = m a \\ F = m a \end{matrix}$

Newtons third law is "If two objects interact they will exert the same amount of force on each other. " This is a statement that forces come in pairs that are exact opposite of one another ( $F_{12} = - F_{21}$ ).

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