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Formulas (master)

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

Physics of Hearing

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

Electric Charge and Electric Field

18. Electric Charge and Electric Field  e≈1.6 x 10⁻¹⁹ C (fundamental charge) ◊  $F=k{\frac {|q_{1}q_{2}|}{r^{2}}}$ (Coulomb's law with k ≈8.99x10⁹ N m² C⁻²) ◊  ${\vec {F}}=q{\vec {E}}$ (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   $\Delta {\text{PE}}=q\Delta V=q(V_{B}-V_{A})$ (potential energy for moving from A to B) ◊  $1eV\approx 1.6\times 10^{-16}{\text{ Joules}}$ (unit conversion) ◊  $E=-\Delta V/\Delta s$ (change in electric potential for small step parallel to electric field) ◊  $V=kQ/r$ (point charge) ◊  $Q=CV$ (capacitor charge)  ◊  $C=\varepsilon _{0}A/d$ (parallel plate with ε₀ = 8.85×10⁻¹²F/m) ◊  ε=κε₀ (dielectric correction) ◊  ${\frac {1}{C_{S}}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+{\frac {1}{C_{3}}}+\dots$ (series) ◊  $C_{p}=C_{1}+C_{2}+C_{3}+\dots$ (parallel) ◊  $E_{cap}={\tfrac {1}{2}}QV={\tfrac {1}{2}}CV^{2}=Q^{2}/(2C)$ (stored energy)

Electric Current, Resistance, and Ohm's Law

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

Circuits and DC Instruments

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

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Magnetism

Magnetism  ◊ hi