OpenStax College Physics/Formulas (master)

Introduction

Introduction  ◊hello 

Kinematics

Kinematics  ◊hello  =====Two-Dimensional Kinematics=====Two-Dimensional Kinematics  ◊hello  =====Dynamics: Force and Newton's Laws of Motion=====Dynamics: Force and Newton's Laws of Motion  ◊hello  =====Further Applications of Newton's Laws: Friction, Drag, and Elasticity=====Further Applications of Newton's Laws: Friction, Drag, and Elasticity  ◊hello  =====Uniform Circular Motion and Gravitation=====Uniform Circular Motion and Gravitation  ◊hello  =====Work, Energy, and Energy Resources=====Work, Energy, and Energy Resources  ◊hello  =====Linear Momentum and Collisions=====Linear Momentum and Collisions  ◊hello  =====Statics and Torque=====Statics and Torque  ◊hello  =====Rotational Motion and Angular Momentum=====Rotational Motion and Angular Momentum  ◊hello  =====Fluid Statics=====Fluid Statics  ◊hello  =====Fluid Dynamics and Its Biological and Medical Applications=====Fluid Dynamics and Its Biological and Medical Applications  ◊hello  =====Temperature, Kinetic Theory, and the Gas Laws=====Temperature, Kinetic Theory, and the Gas Laws  ◊hello  =====Heat and Heat Transfer Methods=====Heat and Heat Transfer Methods  ◊hello  =====Thermodynamics=====Thermodynamics  ◊hello 

Oscillatory Motion and Waves

16. Oscillatory Motion and Waves  ${\displaystyle F=-kx}$ (Hooke's law)  ◊  ${\displaystyle PE_{el}={\tfrac {1}{2}}kx^{2}}$ (Spring energy) ◊  ${\displaystyle fT=1}$ (frequency-period) ◊  ${\displaystyle \omega \equiv 2\pi /T={\sqrt {k/m}}{\text{ or }}{\sqrt {g/L}}}$ (mass/spring or simple pendulum) ◊  ${\displaystyle x=X\cos(\omega t),}$  ${\displaystyle v=-\omega X\sin(\omega t),}$  ${\displaystyle a=-\omega ^{2}X\cos(\omega t)}$ (simple harmonic motion) ◊  ${\displaystyle f\lambda =v_{w}}$ (wave speed) ◊  ${\displaystyle f_{B}=|f_{1}-f_{2}|}$ (beat frequency)

Physics of Hearing

17. Physics of Hearing   ${\displaystyle v_{w}=f\lambda \approx ({\text{331m/s}}){\sqrt {T/{\text{273K}}}}}$ (sound speed) ◊  ${\displaystyle I=P/A=(\Delta p)^{2}/(2\rho v_{w})}$ (sound intensity) ◊  ${\displaystyle \beta {\text{(dB)}}=10\log _{10}(I/I_{0})}$ (I₀ = 10^-12W/m² is the hearing threshold level) ◊  ${\displaystyle f_{obs}=f_{s}\left({\frac {v_{w}}{v_{w}\pm v_{s}}}\right)}$ (+/- for motion (away/towards) stationary observer) ◊  ${\displaystyle f_{obs}=f_{s}\left({\frac {v_{w}\pm v_{obs}}{v_{w}}}\right)}$ (+/- for motion (towards/away from stationary source) ◊  ${\displaystyle f_{n}=n{\frac {v_{w}}{4L}}}$ ${\displaystyle n=1,3,5...}$ (one end closed) ◊  ${\displaystyle f_{n}=n{\frac {v_{w}}{2L}}}$ ${\displaystyle n=1,2,3...}$ (both ends open) ◊  ${\displaystyle a=(Z_{2}-Z_{1})^{2}/(Z_{1}+Z_{2})^{2}}$ (intensity reflection coefficient with acoustical impedance ${\displaystyle Z=\rho v_{w}}$)

Electric Charge and Electric Field

18. Electric Charge and Electric Field  e≈1.6 x 10⁻¹⁹ C (fundamental charge) ◊  ${\displaystyle F=k{\frac {|q_{1}q_{2}|}{r^{2}}}}$ (Coulomb's law with k ≈8.99x10⁹ N m² C⁻²) ◊  ${\displaystyle {\vec {F}}=q{\vec {E}}}$ (Force law with E =kq/r² for the electric field due to a point charge)

Electric Potential and Electric Field

19. Electric Potential and Electric Field   ${\displaystyle \Delta {\text{PE}}=q\Delta V=q(V_{B}-V_{A})}$ (potential energy for moving from A to B) ◊  ${\displaystyle 1eV\approx 1.6\times 10^{-16}{\text{ Joules}}}$ (unit conversion) ◊  ${\displaystyle E=-\Delta V/\Delta s}$ (change in electric potential for small step parallel to electric field) ◊  ${\displaystyle V=kQ/r}$ (point charge) ◊  ${\displaystyle Q=CV}$ (capacitor charge)  ◊  ${\displaystyle C=\varepsilon _{0}A/d}$ (parallel plate with ε₀ = 8.85×10⁻¹²F/m) ◊  ε=κε₀ (dielectric correction) ◊  ${\displaystyle {\frac {1}{C_{S}}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+{\frac {1}{C_{3}}}+\dots }$ (series) ◊  ${\displaystyle C_{p}=C_{1}+C_{2}+C_{3}+\dots }$ (parallel) ◊  ${\displaystyle E_{cap}={\tfrac {1}{2}}QV={\tfrac {1}{2}}CV^{2}=Q^{2}/(2C)}$ (stored energy)

Electric Current, Resistance, and Ohm's Law

20. Electric Current, Resistance, and Ohm's Law   ${\displaystyle I=\Delta Q/\Delta t}$ (current:(1A≡1C/s) ◊  ${\displaystyle I=nqAv_{d}}$ (current and drift velocity) ◊  ${\displaystyle V=IR}$ (Ohm's law: 1Ω=1V/A) ◊  ${\displaystyle R=\rho L/A}$ (resistivity and resistance) ◊  ${\displaystyle \rho =\rho _{0}+\alpha \Delta T}$ (temperature coefficient) ◊  ${\displaystyle P=IV=I^{2}R=V^{2}/R}$ (power as energy/time) ◊  ${\displaystyle P_{\text{ave}}=I_{\text{rms}}V_{\text{rms}}=I_{\text{rms}}^{2}R=V_{\text{rms}}^{2}/R}$ ([alternating current) ◊ ${\displaystyle X_{\text{rms}}={\tfrac {1}{\sqrt {2}}}X_{0}}$ (rms and peak value) ${\displaystyle X(t)=X_{0}\sin(2\pi ft)}$)

Circuits and DC Instruments

21. Circuits and DC Instruments  ◊  ${\displaystyle R_{s}=R_{1}+R_{2}+R_{3}+\ldots }$ (series)  ◊  ${\displaystyle R_{eq}^{-1}=}$ ${\displaystyle R_{1}^{-1}+R_{2}^{-1}+R_{3}^{-1}+\ldots }$ (parallel) ◊  ${\displaystyle V_{\text{terminal}}={\text{emf}}-Ir}$ (terminal voltage, emf, internal resistance)  ◊  ${\displaystyle \Sigma I_{\text{out}}=\Sigma I_{\text{in}}}$ and ${\displaystyle \Sigma \Delta V=0}$ (Kirchhoff's rules: ${\displaystyle \Delta V>0}$ if path from − to + voltage or opposite current through resistor  ◊  ${\displaystyle \tau =RC}$ (RC time): ${\displaystyle V={\text{emf}}\,(1-e^{-t/RC})}$ (charging) ◊  ${\displaystyle V={\text{emf}}\,e^{-t/RC}}$ (discharging)

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