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Formulas (master)

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Introduction

<section begin=Introduction/>IntroductionTemplate:Spaces◊helloTemplate:Spaces<section end=Introduction/>

Kinematics

<section begin=Kinematics/>KinematicsTemplate:Spaces◊helloTemplate:Spaces<section end=Kinematics/> =====Two-Dimensional Kinematics=====<section begin=Two-Dimensional Kinematics/>Two-Dimensional KinematicsTemplate:Spaces◊helloTemplate:Spaces<section end=Two-Dimensional Kinematics/> =====Dynamics: Force and Newton's Laws of Motion=====<section begin=Dynamics: Force and Newton's Laws of Motion/>Dynamics: Force and Newton's Laws of MotionTemplate:Spaces◊helloTemplate:Spaces<section end=Dynamics: Force and Newton's Laws of Motion/> =====Further Applications of Newton's Laws: Friction, Drag, and Elasticity=====<section begin=Further Applications of Newton's Laws: Friction, Drag, and Elasticity/>Further Applications of Newton's Laws: Friction, Drag, and ElasticityTemplate:Spaces◊helloTemplate:Spaces<section end=Further Applications of Newton's Laws: Friction, Drag, and Elasticity/> =====Uniform Circular Motion and Gravitation=====<section begin=Uniform Circular Motion and Gravitation/>Uniform Circular Motion and GravitationTemplate:Spaces◊helloTemplate:Spaces<section end=Uniform Circular Motion and Gravitation/> =====Work, Energy, and Energy Resources=====<section begin=Work, Energy, and Energy Resources/>Work, Energy, and Energy ResourcesTemplate:Spaces◊helloTemplate:Spaces<section end=Work, Energy, and Energy Resources/> =====Linear Momentum and Collisions=====<section begin=Linear Momentum and Collisions/>Linear Momentum and CollisionsTemplate:Spaces◊helloTemplate:Spaces<section end=Linear Momentum and Collisions/> =====Statics and Torque=====<section begin=Statics and Torque/>Statics and TorqueTemplate:Spaces◊helloTemplate:Spaces<section end=Statics and Torque/> =====Rotational Motion and Angular Momentum=====<section begin=Rotational Motion and Angular Momentum/>Rotational Motion and Angular MomentumTemplate:Spaces◊helloTemplate:Spaces<section end=Rotational Motion and Angular Momentum/> =====Fluid Statics=====<section begin=Fluid Statics/>Fluid StaticsTemplate:Spaces◊helloTemplate:Spaces<section end=Fluid Statics/> =====Fluid Dynamics and Its Biological and Medical Applications=====<section begin=Fluid Dynamics and Its Biological and Medical Applications/>Fluid Dynamics and Its Biological and Medical ApplicationsTemplate:Spaces◊helloTemplate:Spaces<section end=Fluid Dynamics and Its Biological and Medical Applications/> =====Temperature, Kinetic Theory, and the Gas Laws=====<section begin=Temperature, Kinetic Theory, and the Gas Laws/>Temperature, Kinetic Theory, and the Gas LawsTemplate:Spaces◊helloTemplate:Spaces<section end=Temperature, Kinetic Theory, and the Gas Laws/> =====Heat and Heat Transfer Methods=====<section begin=Heat and Heat Transfer Methods/>Heat and Heat Transfer MethodsTemplate:Spaces◊helloTemplate:Spaces<section end=Heat and Heat Transfer Methods/> =====Thermodynamics=====<section begin=Thermodynamics/>ThermodynamicsTemplate:Spaces◊helloTemplate:Spaces<section end=Thermodynamics/>

Oscillatory Motion and Waves

<section begin=Oscillatory Motion and Waves/> 16. Oscillatory Motion and WavesTemplate:Spaces$F=-kx$ (Hooke's law) Template:Spaces◊Template:Spaces $P{E}_{el}=\frac{1}{2}k{x}^2$ (Spring energy)Template:Spaces◊Template:Spaces $fT=1$ (frequency-period)Template:Spaces◊Template:Spaces $\omega \equiv 2\pi /T=\sqrt{k/m}\text{ or }\sqrt{g/L}$ (mass/spring or simple pendulum)Template:Spaces◊Template:Spaces $x=X\cos (\omega t),$Template:Spaces$v=-\omega X\sin (\omega t),$Template:Spaces$a=-{\omega }^{2}X\cos (\omega t)$ (simple harmonic motion)Template:Spaces◊Template:Spaces $f\lambda =v_w$ (wave speed)Template:Spaces◊Template:Spaces $f_B=|f_1-f_2|$ (beat frequency) <section end=Oscillatory Motion and Waves/>

Physics of Hearing

<section begin=Physics of Hearing/> 17. Physics of HearingTemplate:Spaces $v_w=f\lambda \approx (\text{331m/s})\sqrt{T/\text{273K}}$ (sound speed)Template:Spaces◊Template:Spaces $I=P/A=(\mathrm{\Delta }p{)}^2/(2\rho v_w)$ (sound intensity)Template:Spaces◊Template:Spaces $\beta \text{(dB)}=10{\log }_{10}(I/I_0)$ (I₀ = 10^-12W/m² is the hearing threshold level)Template:Spaces◊Template:Spaces $f_{obs}=f_s\left(\frac{v_w}{v_w\pm v_s}\right)$ (+/- for motion (away/towards) stationary observer)Template:Spaces◊Template:Spaces $f_{obs}=f_s\left(\frac{v_w\pm v_{obs}}{v_w}\right)$ (+/- for motion (towards/away from stationary source)Template:Spaces◊Template:Spaces $f_n=n\frac{v_w}{4L}$ $n=1,3,5...$ (one end closed)Template:Spaces◊Template:Spaces $f_n=n\frac{v_w}{2L}$ $n=1,2,3...$ (both ends open)Template:Spaces◊Template:Spaces $a=(Z_2-Z_1{)}^2/(Z_1+Z_2{)}^2$ (intensity reflection coefficient with acoustical impedance $Z=\rho v_w$) <section end=Physics of Hearing/>

Electric Charge and Electric Field

<section begin=Electric Charge and Electric Field/> 18. Electric Charge and Electric FieldTemplate:Spacese≈1.6 x 10⁻¹⁹ C (fundamental charge)Template:Spaces◊Template:Spaces $F=k\frac{|q_1{q}_2|}{r^2}$ (Coulomb's law with k ≈Template:Nowrap begin8.99x10⁹ N m² C⁻²Template:Nowrap end)Template:Spaces◊Template:Spaces $\overrightarrow{F}=q\overrightarrow{E}$ (Force law with E =kq/r² for the electric field due to a point charge) <section end=Electric Charge and Electric Field/>

Electric Potential and Electric Field

<section begin=Electric.C2.A0Potential and Electric Field/> 19. Electric Potential and Electric FieldTemplate:Spaces $\mathrm{\Delta }\text{PE}=q\mathrm{\Delta }V=q(V_B-V_A)$ (potential energy for moving from A to B)Template:Spaces◊Template:Spaces $1eV\approx 1.6\times 10^{-16}\text{ Joules}$ (unit conversion)Template:Spaces◊Template:Spaces $E=-\mathrm{\Delta }V/\mathrm{\Delta }s$ (change in electric potential for small step parallel to electric field)Template:Spaces◊Template:Spaces $V=kQ/r$ (point charge)Template:Spaces◊Template:Spaces $Q=CV$ (capacitor charge) Template:Spaces◊Template:Spaces $C={\epsilon }_{0}A/d$ (parallel plate with ε₀ = Template:Nowrap)Template:Spaces◊Template:Spaces ε=κε₀ (dielectric correction)Template:Spaces◊Template:Spaces $\frac{1}{C_S}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\dots$ (series)Template:Spaces◊Template:Spaces $C_p=C_1+C_2+C_3+\dots$ (parallel)Template:Spaces◊Template:Spaces $E_{cap}=\frac{1}{2}QV=\frac{1}{2}C{V}^2=Q^2/(2C)$ (stored energy) <section end=Electric.C2.A0Potential and Electric Field/>

Electric Current, Resistance, and Ohm's Law

<section begin=Electric.C2.A0Current, Resistance, and Ohm's Law/> 20. Electric Current, Resistance, and Ohm's Law Template:Spaces$I=\mathrm{\Delta }Q/\mathrm{\Delta }t$ (current:(1A≡1C/s)Template:Spaces◊Template:Spaces $I=nqA{v}_d$ (current and drift velocity)Template:Spaces◊Template:Spaces $V=IR$ (Ohm's law: 1Ω=1V/A)Template:Spaces◊Template:Spaces $R=\rho L/A$ (resistivity and resistance)Template:Spaces◊Template:Spaces $\rho ={\rho }_0+\alpha \mathrm{\Delta }T$ (temperature coefficient)Template:Spaces◊Template:Spaces $P=IV=I^{2}R=V^2/R$ (power as energy/time)Template:Spaces◊Template:Spaces $P_{\text{ave}}=I_{\text{rms}}{V}_{\text{rms}}=I_{\text{rms}}^{2}R=V_{\text{rms}}^2/R$ ([alternating current)Template:Spaces◊Template:Spaces$X_{\text{rms}}=\frac{1}{\sqrt{2}}{X}_0$ (rms and peak value) $X(t)=X_0\sin (2\pi ft)$) <section end=Electric.C2.A0Current, Resistance, and Ohm's Law/>

Circuits and DC Instruments

<section begin=Circuits and DC Instruments/>21. Circuits and DC InstrumentsTemplate:Spaces◊Template:Spaces $R_s=R_1+R_2+R_3+\dots$ (series) Template:Spaces◊Template:Spaces $R_{eq}^{-1}=$ $R_1^{-1}+R_2^{-1}+R_3^{-1}+\dots$ (parallel)Template:Spaces◊Template:Spaces $V_{\text{terminal}}=\text{emf}-Ir$ (terminal voltage, emf, internal resistance) Template:Spaces◊Template:Spaces $\mathrm{\Sigma }{I}_{\text{out}}=\mathrm{\Sigma }{I}_{\text{in}}$ and $\mathrm{\Sigma }\mathrm{\Delta }V=0$ (Kirchhoff's rules: $\mathrm{\Delta }V>0$ if path from − to + voltage or opposite current through resistor Template:Spaces◊Template:Spaces $\tau =RC$ (RC time): $V=\text{emf}(1-e^{-t/RC})$ (charging)Template:Spaces◊Template:Spaces $V=\text{emf}{e}^{-t/RC}$ (discharging) <section end=Circuits and DC Instruments/>

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hello <section end=Circuits and DC Instruments/>

Magnetism

<section begin=Magnetism/> MagnetismTemplate:Spaces◊Template:Spaceshi <section end=Magnetism/>