List of elementary physics formulae

A list of elementary physics formulae commonly appearing in high-school and college introductory physics courses. The list consists primarily of formulas concerning mechanics, showing relations between matter, energy, motion, and force in Euclidean space, under the action of Newtonian mechanics.

Meanings of symbols

$a,$: acceleration

$A,$: area or amplitude

$E,$: energy

$F,$: force

$sum\; F$: net force

$f\_k,$: kinetic friction force

$f\_s,$: static friction force

$g,$: acceleration due to gravity

$J,$: Impulse

$KE,$: kinetic energy

$m,$: mass

$mu\_k,$: coefficient of kinetic friction

$mu\_s,$: coefficient of static friction

$N,$: Normal force to a surface

$u\; ,$: Frequency

$vec\{p\}$: Momentum

$P,$: Power

$Q,$: heat or flowrate

$r,$: radius

$vec\{s\},$: Distance traveled

$T,$: Period

$t,$: time

$heta,$: Angle (see annotations next to each individual formula for details)

$U\_g,$: gravitational potential energy

$V,$: volume

$V\_\{df\},$: volume of displaced fluid

$v\_f,$: final velocity

$v\_i,$: initial velocity

$x\_f,$: final position

$x\_i,$: initial position

Kinematics

Kinematics formulae compare an object's position, velocity, and acceleration, without taking into consideration its mass or forces around it.:$x\_f\; =\; x\_i\; +\; frac\{(v\_i+v\_f)\}\{2\}t$ (constant acceleration):$x\_f\; =\; x\_i\; +\; \{v\_i\}\{t\}\; +\; frac\{1\}\{2\}\{at^2\}$ (constant acceleration):$x\_f\; =\; x\_i\; +\; \{v\_f\}\{t\}\; -\; frac\{1\}\{2\}\{at^2\}$ (constant acceleration):$v\_f^2\; =\; v\_i^2\; +\; \{2a\}\{(\; x\_f\; -\; x\_i\; )\}$ (constant acceleration):$v\; =\; frac\{dx\}\{dt\}$

Dynamics

Like kinematics, dynamics deal with motion, but take into consideration force and mass.:$\{sum\; F\}\; =\; ma,$ -- Newton's second law:$N\; =\; mgcos\; heta,$ ($heta,$ is the angle between the supporting surface and the vertical):$f\_k\; =\; \{mu\_k\}N,$ (object moving relative to surface):$f\_s\; =\; \{mu\_s\}N,$ (object not moving relative to surface)

Work, energy and power

Work, energy, and power describes an objects ability to affect nature.:$W\; =\; int\; vec\{F\}\; cdot\; dvec\{s\}$ -- definition of mechanical work:$KE\; =\; frac\{1\}\{2\}\{mv^2\},!$ -- definition of kinetic energy:$W\; =\; Delta\; \{KE\},!$ -- theorem of the kinetic energy:$W\; =\; -Delta\; \{U\},!$:$U\_g\; =\; mgh\; ,!$:$E\; =\; KE\; +\; U\; ,!$:$P\; =\; frac\{dE\}\{dt\}\; =\; int\; vec\{F\}cdot\; vec\{v\}\; ,!$:$P\_\{avg\}\; =\; frac\{Delta\; E\}\{Delta\; t\},!$

Simple Harmonic Motion

These are mechanics formulae that deal with simple harmonic motion.:$F\; =\; -kx,!$ ($k,$ is the spring constant) -- Hooke's law:$T\_\{spring\}\; =\; 2pisqrt\{frac\{m\}\{k,!$:$u\; =\; frac\{1\}\{T\},!$:$U\_s\; =\; frac\{1\}\{2\}kx^2,!$ ($k,$ is the spring constant):$v\_\{maxspring\}\; =\; xsqrt\{frac\{k\}\{m,!$:$T\_\{pendulum\}\; =\; 2pisqrt\{frac\{L\}\{g,!$ (for a simple pendulum)

Momentum

Momentum is the amount of mass moving, in classical mechanics.:$vec\{p\}\; =\; mvec\{v\}\; ,!$ -- definition of momentum:$J\; =\; int\; F\; ,dt$ -- definition of impulse:$J\; =\; Delta\; p\; ,!$:$m\_1vec\{v\_1\}\; +\; m\_2vec\{v\_2\}\; =\; m\_1vec\{v\_1\text{'}\}\; +\; m\_2vec\{v\_2\text{'}\}\; ,!$ -- conservation of momentum:$frac\{1\}\{2\}m\_1v\_1^2\; +\; frac\{1\}\{2\}m\_2v\_2^2\; =\; frac\{1\}\{2\}m\_1v\_1\text{'}^2\; +\; frac\{1\}\{2\}m\_2v\_2\text{'}^2\; ,!$ (Note: this is only true for elastic collisions)

Uniform circular Motion and Gravitation

An object moving along a circular path at constant speed is in uniform circular motion. In this section, $a\_c$, $F\_c$, et cetera, stand for centripetal acceleration and force, respectively.:$a\_c\; =\; frac\{v^2\}\{r\}\; =\; frac\{4pi^2r\}\{t^2\},!$:$F\_c\; =\; frac\{mv^2\}\{r\},!$:$F\_g\; =\; Gfrac\{m\_1m\_2\}\{r^2\},!$:$a\_\{gravity\}\; =\; Gfrac\{m\_\{planet\{r^2\},!$:$v\_\{satellite\}\; =\; sqrt\{frac\{Gm\_\{planet\{R$:$U\_\{gravitational\}\; =\; Gfrac\{m\_1m\_2\}\{r\}$:$KE\_\{satellite\}\; =\; Gfrac\{m\_sm\_\{planet\{2R\}$:$E\_\{satellite\}\; =\; -Gfrac\{m\_sm\_\{planet\{2R\}$:$frac\{T\_1^2\}\{a\_1^3\}\; =\; frac\{T\_2^2\}\{a\_2^3\}$

Thermodynamics

Thermodynamics deal with the energy, motion, and entropy of microscopic particles.

:$Q\; =\; mc\; Delta\; T\; ,!$:$Delta\; L\; =\; L\_i\; alpha\; Delta\; T\; ,!$::$PV\; =\; nRT\; ,!$:$frac\{P\_iV\_i\}\{T\_i\}\; =\; frac\{P\_fV\_f\}\{T\_f\}\; ,!$:$Delta\; U\; =\; Delta\; Q\; +\; Delta\; T\; ,!$:$e\; =\; 1-frac\{Delta\; Q\_\{out\{Delta\; Q\_\{in\; ,!$

Rotational Motion

:

Fluids

:$F\_\{buoyancy\}\; =\; ho\; g\; V\_\{df\},$:$p\; =\; p\_\{atmospheric\}\; +\; ho\; g\; h,$:$p\; =\; frac\{F\}\{a\},!$:$Q\; =\; Av,!$