Physics Formulas

Meanings of the 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
$\nu \,$ : Frequency
$\vec{p}$ : Momentum
$P\,$ : Power
$Q\,$ : heat or flowrate
$r\,$ : radius
$\vec{s}\,$ : Distance traveled
$T\,$ : Period, Temperature
$t\,$ : time
$\theta\,$ : Angle (see annotations next to each individual formula for details)
$U_g\,$ : gravitational potential energy
$V\,$ : volume
$V_{df}\,$ : volume of displaced fluid
$v_f\,$ : initial velocity

V o

: final velocity
$x_f\,$ : final position
$x_i\,$ : initial position

Dynamics

Like kinematics, dynamics deal with motion, but take into consideration force and mass.

${\sum F} = ma\,\$ -- Newton's second law

$N = mg\cos \theta\,$ ( $\theta\,$ 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.

$W = \int \vec{F} \cdot d\vec{s}$ -- definition of mechanical work

$W = \Delta {KE}\,\!$

$W = -\Delta {U}\,\!$

$U_g = mgh \,\!$

$E = KE + U \,\!$

$KE = \frac{1}{2}{mv^2}\,\!$

$P = \frac{dE}{dt} = \int \vec{F}\cdot \vec{v} \,\!$

$P_{avg} = \frac{\Delta E}{\Delta t}\,\!$

Simple Harmonic Motion

These are mechanics formulae that deal with simple harmonic motion.

$F = -kx\,\!$ ( $k\,$ is the spring constant) -- Hooke's law

$T_{spring} = (1/2\pi)\sqrt{\frac{m}{k}}\,\!$

$\nu = \frac{1}{T}\,\!$

$U_s = \frac{1}{2}kx^2\,\!$ ( $k\,$ is the spring constant)

$v_{maxspring} = x\sqrt{\frac{k}{m}}\,\!$

$T_{pendulum} = 2\pi\sqrt{\frac{L}{g}}\,\!$ (for a simple pendulum)

Momentum

Momentum is the amount of mass moving, in classical mechanics.

$\vec{p} = m\vec{v} \,\!$ -- definition of momentum

$J = \int F \,dt$ -- definition of impulse

$J = \Delta p \,\!$

$m_1\vec{v_1} + m_2\vec{v_2} = m_1\vec{v_1'} + m_2\vec{v_2'} \,\!$ -- conservation of momentum

$\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 = \frac{1}{2}m_1v_1'^2 + \frac{1}{2}m_2v_2'^2 \,\!$ (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.

$a_c = \frac{v^2}{r} = \frac{4\pi^2r}{t^2}\,\!$

$F_c = \frac{mv^2}{r}\,\!$

$F_g = G\frac{m_1m_2}{r^2}\,\!$

$a_{gravity} = G\frac{m_{planet}}{r^2}\,\!$

$v_{satellite} = \sqrt{\frac{Gm_{planet}}{R}}$

$U_{gravitational} = G\frac{m_1m_2}{r}$

$KE_{satellite} = G\frac{m_sm_{planet}}{2R}$

$E_{satellite} = -G\frac{m_sm_{planet}}{2R}$

$\frac{T_1^2}{a_1^3} = \frac{T_2^2}{a_2^3}$

Thermodynamics

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

$Q = mc \Delta T \,\!$

$\Delta L = L_i \alpha \Delta T \,\!$

$\Delta V = V_i \beta \Delta T \,\!$

$PV = nRT \,\!$

$\frac{P_iV_i}{T_i} = \frac{P_fV_f}{T_f} \,\!$

$\Delta U = \Delta Q + \Delta T \,\!$

$e = 1-\frac{\Delta Q_{out}}{\Delta Q_{in}} \,\!$

Rotational Motion

$\boldsymbol \tau=rF \sin \theta$

Fluids

$F_{buoyancy} = \rho g V_{df}\,$

$p = p_{atmospheric} + \rho g h\,$

$p = \frac{F}{a}\,\!$

$Q = Av\,\!$

$P + \rho gh + \frac{1}{2} \rho v^2 = k$

p V = k

$\frac{P}{T}=k$

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