View source for OpenStax College Physics/Formulas (master)

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|<small>[[OpenStax_College_Physics/Equations_(master)|Equations (master)]]</small>
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|<small>[[OpenStax_College_Physics/Formulas (master)|Formulas (master)]]</small>
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|<small>[[OpenStax_College_Physics/Equations|Equations]]</small>
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|<small>[[OpenStax_College_Physics/Formulas|Formulas]]</small>
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|<small>[[OpenStax/Flexible equation transclusion|Help]]</small>
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=====Introduction=====
<section begin=Introduction/>'''[[OpenStax_College_Physics/Equations_(master)#Introduction|Introduction]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Introduction/>
=====Kinematics=====
<section begin=Kinematics/>'''[[OpenStax_Physics/College/Equations_(master)#Kinematics|Kinematics]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Kinematics/>
=====Two-Dimensional Kinematics=====<section begin=Two-Dimensional Kinematics/>'''[[OpenStax_Physics/College/Equations_(master)#Two-Dimensional Kinematics|Two-Dimensional Kinematics]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Two-Dimensional Kinematics/>
=====Dynamics: Force and Newton's Laws of Motion=====<section begin=Dynamics: Force and Newton's Laws of Motion/>'''[[OpenStax_Physics/College/Equations_(master)#Dynamics: Force and Newton's Laws of Motion|Dynamics: Force and Newton's Laws of Motion]]'''{{spaces|2}}&loz;hello{{spaces|1}}<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/>'''[[OpenStax_Physics/College/Equations_(master)#Further Applications of Newton's Laws: Friction, Drag, and Elasticity|Further Applications of Newton's Laws: Friction, Drag, and Elasticity]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Further Applications of Newton's Laws: Friction, Drag, and Elasticity/>
=====Uniform Circular Motion and Gravitation=====<section begin=Uniform Circular Motion and Gravitation/>'''[[OpenStax_Physics/College/Equations_(master)#Uniform Circular Motion and Gravitation|Uniform Circular Motion and Gravitation]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Uniform Circular Motion and Gravitation/>
=====Work, Energy, and Energy Resources=====<section begin=Work, Energy, and Energy Resources/>'''[[OpenStax_Physics/College/Equations_(master)#Work, Energy, and Energy Resources|Work, Energy, and Energy Resources]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Work, Energy, and Energy Resources/>
=====Linear Momentum and Collisions=====<section begin=Linear Momentum and Collisions/>'''[[OpenStax_Physics/College/Equations_(master)#Linear Momentum and Collisions|Linear Momentum and Collisions]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Linear Momentum and Collisions/>
=====Statics and Torque=====<section begin=Statics and Torque/>'''[[OpenStax_Physics/College/Equations_(master)#Statics and Torque|Statics and Torque]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Statics and Torque/>
=====Rotational Motion and Angular Momentum=====<section begin=Rotational Motion and Angular Momentum/>'''[[OpenStax_Physics/College/Equations_(master)#Rotational Motion and Angular Momentum|Rotational Motion and Angular Momentum]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Rotational Motion and Angular Momentum/>
=====Fluid Statics=====<section begin=Fluid Statics/>'''[[OpenStax_Physics/College/Equations_(master)#Fluid Statics|Fluid Statics]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Fluid Statics/>
=====Fluid Dynamics and Its Biological and Medical Applications=====<section begin=Fluid Dynamics and Its Biological and Medical Applications/>'''[[OpenStax_Physics/College/Equations_(master)#Fluid Dynamics and Its Biological and Medical Applications|Fluid Dynamics and Its Biological and Medical Applications]]'''{{spaces|2}}&loz;hello{{spaces|1}}<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/>'''[[OpenStax_Physics/College/Equations_(master)#Temperature, Kinetic Theory, and the Gas Laws|Temperature, Kinetic Theory, and the Gas Laws]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Temperature, Kinetic Theory, and the Gas Laws/>
=====Heat and Heat Transfer Methods=====<section begin=Heat and Heat Transfer Methods/>'''[[OpenStax_Physics/College/Equations_(master)#Heat and Heat Transfer Methods|Heat and Heat Transfer Methods]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Heat and Heat Transfer Methods/>
=====Thermodynamics=====<section begin=Thermodynamics/>'''[[OpenStax_Physics/College/Equations_(master)#Thermodynamics|Thermodynamics]]'''{{spaces|2}}&loz;hello{{spaces|1}}<section end=Thermodynamics/>

=====Oscillatory Motion and Waves=====
<section begin=Oscillatory Motion and Waves/>
'''[[OpenStax_College_Physics/Equations_(master)#Oscillatory Motion and Waves|16. Oscillatory Motion and Waves]]'''{{spaces|2}}<math>F=-kx</math> (Hooke's law) {{spaces|1}}&loz;{{spaces|1}}
<math>PE_{el}=\tfrac 1 2 kx^2</math> (Spring energy){{spaces|1}}&loz;{{spaces|1}}
<math>fT=1</math> (frequency-period){{spaces|1}}&loz;{{spaces|1}}
<math>\omega\equiv 2\pi/T = \sqrt{k/m}\text{ or }\sqrt{g/L}</math> (mass/spring or simple pendulum){{spaces|1}}&loz;{{spaces|1}}
<math>x=X\cos(\omega t),</math>{{spaces|2}}<math> v=-\omega X\sin(\omega t),</math>{{spaces|2}}<math> a=-\omega^2 X \cos(\omega t)</math> (simple harmonic motion){{spaces|1}}&loz;{{spaces|1}}
<math>f\lambda = v_{w}</math> (wave speed){{spaces|1}}&loz;{{spaces|1}}
<math>f_B=|f_1-f_2|</math> (beat frequency)
<section end=Oscillatory Motion and Waves/>

=====Physics of Hearing=====
<section begin=Physics of Hearing/>
'''[[OpenStax_College_Physics/Equations_(master)#Physics of Hearing|17. Physics of Hearing]]'''{{spaces|2}}
<math>v_w=f\lambda\approx(\text{331m/s})\sqrt{T/\text{273K}}</math> (sound speed){{spaces|1}}&loz;{{spaces|1}}
<math>I=P/A=(\Delta p)^2/(2\rho v_w)</math> (sound intensity){{spaces|1}}&loz;{{spaces|1}}
<math>\beta \text{(dB)}= 10\log_{10}(I/I_0)</math> (''I<sub>0</sub>'' = 10<sup>-12</sup>W/m<sup>2</sup> is the hearing threshold level){{spaces|1}}&loz;{{spaces|1}}
<math>f_{obs}=f_s\left(\frac{v_w}{v_w\pm v_s}\right)</math> (+/- for motion (away/towards) stationary observer){{spaces|1}}&loz;{{spaces|1}}
<math>f_{obs}=f_s\left(\frac{v_w\pm v_{obs}}{v_w}\right)</math> (+/- for motion (towards/away from stationary source){{spaces|1}}&loz;{{spaces|1}} 
<math>f_n=n\frac{v_w}{4L}</math> <math>n=1,3,5...</math> (one end closed){{spaces|1}}&loz;{{spaces|1}}
<math>f_n=n\frac{v_w}{2L}</math> <math>n=1,2,3...</math> (both ends open){{spaces|1}}&loz;{{spaces|1}}
<math>a=(Z_2-Z_1)^2/(Z_1+Z_2)^2</math> (intensity reflection coefficient with acoustical impedance <math>Z=\rho v_w</math>)
<section end=Physics of Hearing/>
=====Electric Charge and Electric Field=====
<section begin=Electric Charge and Electric Field/>
'''[[OpenStax_College_Physics/Equations_(master)#Electric Charge and Electric Field|18. Electric Charge and Electric Field]]{{spaces|2}}''e&asymp;1.6 x 10<sup>&minus;19</sup> C''''' (fundamental charge){{spaces|1}}&loz;{{spaces|1}} 
<math>F=k\frac{|q_1q_2|}{r^2}</math> (Coulomb's law with '''''k &asymp;{{nowrap begin}}8.99x10<sup>9</sup> N m<sup>2</sup> C<sup>&minus;2</sup>{{nowrap end}}'''''){{spaces|1}}&loz;{{spaces|1}} 
<math>\vec F = q\vec E</math> (Force law with '''''E =kq/r<sup>2</sup>'''''  for the electric field due to a point charge)
<section end=Electric Charge and Electric Field/>
=====Electric&nbsp;Potential and Electric Field=====
<section begin=Electric.C2.A0Potential and Electric Field/>
'''[[OpenStax_College_Physics/Equations_(master)#Electric.C2.A0Potential_and_Electric_Field|19. Electric Potential and Electric Field]]{{spaces|2}}'''
<math>\Delta\text{PE}=q\Delta V = q(V_B-V_A)</math> (potential energy for moving from A to B){{spaces|1}}&loz;{{spaces|1}} 
<math>1eV\approx 1.6\times 10^{-16}\text{ Joules}</math> (unit conversion){{spaces|1}}&loz;{{spaces|1}} 
<math>E = -\Delta V/\Delta s</math> (change in electric potential for small step parallel to electric field){{spaces|1}}&loz;{{spaces|1}} 
<math>V=kQ/r</math> (point charge){{spaces|1}}&loz;{{spaces|1}} 
<math>Q=CV</math> (capacitor charge) {{spaces|1}}&loz;{{spaces|1}} 
<math>C=\varepsilon_0 A/d</math> (parallel plate with ''&epsilon;<sub>0</sub>'' = {{nowrap|8.85&times;10<sup>&minus;12</sup>F/m}}){{spaces|1}}&loz;{{spaces|1}} 
&epsilon;=&kappa;&epsilon;<sub>0</sub> (dielectric correction){{spaces|1}}&loz;{{spaces|1}} 
<math>\frac{1}{C_S}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\dots</math> (series){{spaces|1}}&loz;{{spaces|1}} 
<math>C_p=C_1+C_2+C_3+\dots</math> (parallel){{spaces|1}}&loz;{{spaces|1}} 
<math>E_{cap}=\tfrac 1 2 QV =\tfrac 1 2 CV^2 =Q^2/(2C)</math> (stored energy)
<section end=Electric.C2.A0Potential and Electric Field/>

=====Electric&nbsp;Current, Resistance, and Ohm's Law=====
<section begin=Electric.C2.A0Current, Resistance, and Ohm's Law/>
'''[[OpenStax_College_Physics/Equations_(master)#Electric.C2.A0Current.2C_Resistance.2C_and_Ohm.27s_Law|20. Electric Current, Resistance, and Ohm's Law]]''' {{spaces|2}}<math>I=\Delta Q/\Delta t</math> (current:(1A&equiv;1C/s){{spaces|1}}&loz;{{spaces|1}}
<math>I=nqAv_d</math> (current and drift velocity){{spaces|1}}&loz;{{spaces|1}}
<math>V=IR</math> (Ohm's law: 1&Omega;=1V/A){{spaces|1}}&loz;{{spaces|1}}
<math>R=\rho L/A</math> (resistivity and resistance){{spaces|1}}&loz;{{spaces|1}}
<math>\rho=\rho_0 + \alpha\Delta T</math> (temperature coefficient){{spaces|1}}&loz;{{spaces|1}}
<math>P=IV=I^2R=V^2/R</math> ([[w:Power (physics)|power]] as energy/time){{spaces|1}}&loz;{{spaces|1}}
<math>P_\text{ave}=I_\text{rms}V_\text{rms}=I_\text{rms}^2R=V_\text{rms}^2/R</math> ([alternating current){{spaces|1}}&loz;{{spaces|1}}<math>X_\text{rms}=\tfrac{1}{\sqrt 2} X_0</math> (rms and peak value) <math>X(t)=X_0\sin(2\pi ft)</math>)
<section end=Electric.C2.A0Current, Resistance, and Ohm's Law/>

=====Circuits and DC Instruments=====
<section begin=Circuits and DC Instruments/>'''[[OpenStax_College_Physics/Equations_(master)#Circuits and DC Instruments|21. Circuits and DC Instruments]]'''{{spaces|2}}&loz;{{spaces|1}} <math>R_s=R_1+R_2+R_3+\ldots</math> (series) {{spaces|1}}&loz;{{spaces|1}} 
<math>R_{eq}^{-1} = </math> <math> R_1^{-1}+R_2^{-1}+R_3^{-1}+\ldots</math> (parallel){{spaces|1}}&loz;{{spaces|1}}
<math>V_\text{terminal} = \text{emf} -Ir</math> (terminal
voltage, emf, internal resistance) {{spaces|1}}&loz;{{spaces|1}}
<math>\Sigma I_\text{out}=\Sigma I_\text{in}</math> and <math>\Sigma\Delta V = 0</math> (Kirchhoff's rules:  <math>\Delta V > 0</math> if path from &minus; to + voltage or opposite current through resistor {{spaces|1}}&loz;{{spaces|1}} <math>\tau = RC</math> (RC time): <math>V=\text{emf}\,(1-e^{-t/RC})</math> (charging){{spaces|1}}&loz;{{spaces|1}} <math>V=\text{emf}\,e^{-t/RC}</math> (discharging)
<section end=Circuits and DC Instruments/>

==end==
hello
<section end=Circuits and DC Instruments/>

=====Magnetism=====
<section begin=Magnetism/>
'''[[OpenStax_College_Physics/Equations_(master)#Magnetism|Magnetism]]'''{{spaces|2}}&loz;{{spaces|1}}hi
<section end=Magnetism/>

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=====Electromagnetic Induction, AC Circuits, and Electrical Technologie=====<section begin=Electromagnetic Induction, AC Circuits, and Electrical Technologie/>'''[[OpenStax_College_Physics/Equations_(master)#Electromagnetic Induction, AC Circuits, and Electrical Technologie|Electromagnetic Induction, AC Circuits, and Electrical Technologie]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Electromagnetic Induction, AC Circuits, and Electrical Technologie/>
=====Electromagnetic Waves=====<section begin=Electromagnetic Waves/>'''[[OpenStax_College_Physics/Equations_(master)#Electromagnetic Waves|Electromagnetic Waves]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Electromagnetic Waves/>
=====Geometric Optics=====<section begin=Geometric Optics/>'''[[OpenStax_College_Physics/Equations_(master)#Geometric Optics|Geometric Optics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Geometric Optics/>
=====Vision and Optical Instruments=====<section begin=Vision and Optical Instruments/>'''[[OpenStax_College_Physics/Equations_(master)#Vision and Optical Instruments|Vision and Optical Instruments]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Vision and Optical Instruments/>
=====Wave Optics=====<section begin=Wave Optics/>'''[[OpenStax_College_Physics/Equations_(master)#Wave Optics|Wave Optics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Wave Optics/>
=====Special Relativity=====<section begin=Special Relativity/>'''[[OpenStax_College_Physics/Equations_(master)#Special Relativity|Special Relativity]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Special Relativity/>
=====Introduction to Quantum Physics=====<section begin=Introduction to Quantum Physics/>'''[[OpenStax_College_Physics/Equations_(master)#Introduction to Quantum Physics|Introduction to Quantum Physics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Introduction to Quantum Physics/>
=====Atomic Physics=====<section begin=Atomic Physics/>'''[[OpenStax_College_Physics/Equations_(master)#Atomic Physics|Atomic Physics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Atomic Physics/>
=====Radioactivity and Nuclear Physics=====<section begin=Radioactivity and Nuclear Physics/>'''[[OpenStax_College_Physics/Equations_(master)#Radioactivity and Nuclear Physics|Radioactivity and Nuclear Physics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Radioactivity and Nuclear Physics/>
=====Medical Applications of Nuclear Physics=====<section begin=Medical Applications of Nuclear Physics/>'''[[OpenStax_College_Physics/Equations_(master)#Medical Applications of Nuclear Physics|Medical Applications of Nuclear Physics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Medical Applications of Nuclear Physics/>
=====Particle Physics=====<section begin=Particle Physics/>'''[[OpenStax_College_Physics/Equations_(master)#Particle Physics|Particle Physics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Particle Physics/>
=====Frontiers of Physics=====<section begin=Frontiers of Physics/>'''[[OpenStax_College_Physics/Equations_(master)#Frontiers of Physics|Frontiers of Physics]]'''{{spaces|2}}&loz;{{spaces|1}}<section end=Frontiers of Physics/>

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