Forces¶

Newton's Laws of Motion¶

Newton's First Law

An object at rest stays at rest and an object in motion stays in motion at a constant speed and direction unless acted upon by an unbalanced force.

Newton's Second Law

Force equals mass times acceleration. $F=ma$

Newton's Third Law

For every action there is an equal and opposite reaction.

Simple simulation of a helium balloon rising up¶

Friction¶

Friction is a dissipative force. A dissipative force is one in which the total energy of a system decreases when an object is in motion. --- Nature of Code

For friction, kinetic energy (motion) is converted into thermal energy (heat). There are two types of friction:
1. Static friction
2. Kinematic friction

Formula of friction

$\vec{F} = -\mu N \hat{v}$

Explanation

$\vec{F}$ -- resulting force vector
$\mu$ -- coefficient of friction
$N$ -- a scalar that represents the normal force
$\hat{v}$ -- unit vector of the velocity

Air and Fluid Resistance¶

There is apparently also friction when a body passes through a liquid or gas. This force can be called viscous force, drag force, or fluid resistance; fundamentally, they are all the same thing.

Formula for drag force

$\vec{F_d}=-\frac{1}{2}\rho v^2 A C_d \hat{v}$

Explanation

Symbol	Meaning
$\vec{F_d}$	The resulting drag force.
$-\frac{1}{2}$	It's just a constant. What's important is that it's negative, meaning the resulting force is in the opposite direction of the velocity.
$\rho$	The density of the liquid.
$v^2$	$v$ is the speed of the object; it's a scalar.
$A$	The frontal area of the object.
$C_d$	The coefficient of drag.
$\hat{v}$	The unit vector of the velocity.

Gravitational Attraction¶

Formula of gravitational attraction

$\vec{F} = \frac{G m_1 m_2}{r^2}\hat{r}$