Resource: Forces overview

A general brainstorm for relevant and common-seen forces is listed below. Symbols are shown where often used and formulas where known and useful. (Be aware of vector versus magnitude notation, $\vec F$ and $F$, in formulas.) Symbols used:

  • $\mu_k$ and $\mu_s$ are friction coefficients,
  • $k$ the spring constant,
  • $\Delta s$ elongated/compressed length (difference from natural/relaxed length),
  • $C_D$ aerodynamic/drag coefficient,
  • $\rho$ fluid density,
  • $A$ frontal/projected area in direction of motion,
  • $v$ speed and $\vec v$ velocity,
  • $V$ submerged volume,
  • $g$ gravitational acceleration,
  • $m$ and $M$ two different masses,
  • $G$ gravitational constant
  • $r$ distance (orbit radius or charge separation)
  • $q$ and $Q$ two different charges
  • $\vec E$ electric field
  • $\varepsilon_0$ vacuum permittivity
  • $l$ length of wire carrying current $\vec I$
  • $\vec B$ magnetic field
Mechanical forces (internal or needing contact)[1]
Tension$$\vec T$$... in taut strings
Compression... in lifting walls
Normal force$$\vec n$$... when a surface “holds back” against something
Kinetic friction$$\vec f_k$$... between sliding surfaces$$f_k=\mu_k n$$
Static friction$$\vec f_s$$... between surfaces about to slide$$f_s\leq \mu_s n$$
Elastic force /
spring force
(Hooke's law)
$$\vec F_\text{elastic}$$... in stretched rubber bands or pressed springs$$\vec F_\text{elastic}=-k\;\Delta \vec s$$

Other usual forces such as kicking forces, throwing forces, chewing forces, etc. are included in those already listed.

Fluid forces (in liquids or gasses)
Drag[1]$$\vec D$$... on flying planes and sailing submarines$$D=C_D\rho Av^2$$
Buoyancy[1]$$\vec B$$... pushing up the light bathing ring$$B=\rho V g$$
Diffusion[4] 1... causing absorption and mixing
Surface tension /
... causing water to form round rain drops
Field forces (at a distance)[1]
Weight$$\vec w$$... when gravity pulls you down$$w=mg$$
Gravitational force$$\vec F_g$$... when gravity attracts$$F_g=G\frac{mM}{r^2}$$
Electric force
(Coulomb's law)
$$\vec F_e$$... charge attraction and repulsion
$\displaystyle\vec F_e=q\vec E$
$\displaystyle F_e=\frac 1{4\pi\varepsilon_0}\frac{qQ}{r^2}$
Magnetic force$$\vec F_B$$... magnetic pole attraction and repulsion
$\displaystyle\vec F_B=q\vec v\times \vec B$
$\displaystyle \vec F_B=l\vec I\times \vec B$
Strong nuclear force[7]... holds the atom together
Weak nuclear force[7]... causes breakdown of atoms

Weight and the gravitational force are in fact the same thing, we just must input $g=\frac{GM}{r^2}$.

The electric and magnetic forces are usually combined into one electromagnetic force (called the Lorentz’ force): $\vec F_L=q\vec E+q\vec v\times \vec B$.[1]

Chemical forces
Adhesion[11]... when tape sticks and paint adheres
Bonding force2... holding materials together
Capillary force[9]... when liquid by itself sucks into a straw

Many of the forces can be differently categorised, such as intermolecular forces (bonding force, strong nuclear force etc.).


  1. Encyclopædia Britannica’ (encyclopedia), www.britannica.com

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