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Physics Formulae
1.
Physics Formulae for School
Students M. D. Raghu
2.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com 𝒗 = 𝒅 𝒕 𝒂 = ∆𝒗 ∆𝒕 𝒅 = 𝒗𝒊 𝒕 + 𝟏 𝟐 𝒂𝒕 𝟐 𝒗 𝒇 𝟐 = 𝒗𝒊 𝟐 + 𝟐𝒂𝒅 𝒗 𝒇 = 𝒗𝒊 + 𝒂𝒕 Kinematics v: velocity d: distance t: time a: acceleration vi : initial velocity vf : final velocity
3.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Mechanics 𝑭 = 𝒎 𝒂 Т = 𝑭 𝒅 𝑭 = −𝒌 𝒙 𝑬 𝒌 = 𝟏 𝟐 𝒎 𝒗 𝟐 𝑬 𝒑 = 𝒎 𝒈 𝒉 𝑭 = 𝑮 𝒎 𝟏 𝒎 𝟐 𝒅 𝟐 𝑬 𝒑 = −𝑮 𝒎 𝟏 𝒎 𝟐 𝒅 F: force , m: mass a: acceleration Т: torque , d: distance k: spring constant x: spring extension Ep : potential energy g: acceleration due to gravity h: height G: universal gravitational constant Ek : kinetic energy, v: velocity Ep : potential energy
4.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Simple Harmonic Motion 𝑻 = 𝟐𝝅 𝒎 𝒌 𝝎 = 𝟐𝝅𝒇 𝑬 𝒑 = 𝟏 𝟐 𝒌 𝒙 𝟐 𝒗 𝒎𝒂𝒙 = 𝟐𝝅𝑨 𝑻 𝑻 = 𝟐𝝅 𝒍 𝒈 𝒇 = 𝟏 𝑻 m: suspended mass 𝛚: angular velocity v : velocity A: amplitude l: pendulum length g: acceleration due to gravity Ep : elastic potential energy k: spring constant, x: extension f: frequency T: time period
5.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com ⍺ = 𝒗 𝟐 𝒓 ѡ = 𝟐𝝅𝒇 𝒗 = 𝒓 ѡ ѡ 𝒇 𝟐 = ѡ𝒊 𝟐 + 𝟐 ⍺ 𝜽 𝒔 = 𝒓 𝜽 ѡ 𝒇 = ѡ𝒊 + ⍺𝒕 𝜽 = ѡ𝒊t + 𝟏 𝟐 ⍺ 𝒕 𝟐 Circular Motion ⍺: angular acceleration v: linear velocity , r: radius ѡ: angular velocity f: frequency s: linear displacement ѡ𝐢 : initial angular velocity ѡ𝐟 : final angular velocity Θ: angular displacement t: time
6.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Heat 𝑬 𝒉 = 𝒎 𝒄 ∆𝑻 𝑬 𝑳 = 𝒎 𝑳 𝐄 𝐋: latent heat L: specific latent heat 𝐄 𝐡 : heat energy, m: mass c: specific heat capacity ∆𝑻: temperature difference 𝑩𝒂𝒔𝒊𝒄 𝒐𝒓 𝒁𝒆𝒓𝒐𝒆𝒕𝒉 𝑳𝒂𝒘 𝐼𝑓 𝑏𝑜𝑑𝑦 𝐴 𝑎𝑛𝑑 𝑏𝑜𝑑𝑦 𝐵 𝑎𝑟𝑒 𝑖𝑛 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑤𝑖𝑡ℎ 𝑏𝑜𝑑𝑦 𝐶, 𝑡ℎ𝑒𝑛 𝐴 𝑎𝑛𝑑 𝐵 𝑎𝑟𝑒 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑤𝑖𝑡ℎ 𝑒𝑎𝑐ℎ 𝑜𝑡ℎ𝑒𝑟 𝑭𝒊𝒓𝒔𝒕 𝒍𝒂𝒘 𝑸 = ∆𝑼 − 𝑾 Thermodynamics 𝐐: heat energy supplied ∆U: gain in internal energy W: work done on the system
7.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Heat 𝑷 𝟏 𝑽 𝟏 = 𝑷 𝟐 𝑽 𝟐 𝐏 𝟏 : initial pressure 𝐏 𝟐 : final pressure 𝐕 𝟏 : initial volume 𝐕 𝟐 : final volume Boyle’s Law 𝑽 𝟏 𝑻 𝟏 = 𝑽 𝟐 𝑻 𝟐 𝐓 𝟏 : initial temperature 𝐓 𝟐 : final temperature Charle’s Law 𝑷 𝟏 𝑽 𝟏 𝑻 𝟏 = 𝑷 𝟐 𝑽 𝟐 𝑻 𝟐 Ideal Gas Equation
8.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Fluid Mechanics 𝑷 = 𝑭 𝑨 𝑷 𝑯 = 𝝆 𝒈 𝒉 𝑼 𝒕 = 𝒎 𝒅 𝒈 𝑫 = 𝒎 𝑽 P: pressure F: force, A: area 𝐏 𝐇 : hydrostatic pressure 𝝆: liquid density g: acceleration due to gravity h: height of liquid 𝐔𝐭 : upward thrust 𝐦 𝐝: mass of fluid displaced 𝐃 : density 𝐦: mass, V: volume
9.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com 𝟏 𝒇 = 𝟏 𝒖 + 𝟏 𝒗 𝑴 = 𝒉𝒊 𝒉 𝟎 𝒏 = 𝒄𝒊 𝒄 𝒓 𝝀 = 𝒄 𝒇 𝒏𝒊 𝒔𝒊𝒏 𝜽𝒊 = 𝒏 𝒓 𝒔𝒊𝒏 𝜽 𝒓 Light f: focal length u: image distance v: object distance M: magnification hi: image height, ho: object height n: refractive index ci : velocity of incident ray cr : velocity of refracted ray 𝚯𝐢/𝚯 𝐫 : angle of incidence/refraction f: frequency , 𝛌: wavelength c: velocity of light (wave)
10.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com 𝒇 𝒃 = 𝒇 𝟏 − 𝒇 𝟐 𝒇 = 𝟏 𝑻 𝒗 = 𝒇𝝀 Waves fb : beat frequency f1 : frequency of first wave f2 : frequency of second wave f: frequency T : time period v: wave velocity 𝛌: wavelength 𝒇′ = 𝒇 𝒗 𝒘 𝒗 𝒘±𝒗 𝒔 f’ : apparent frequency f: source frequency vw : wave velocity, vs : source velocity Doppler Effect
11.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com 𝝀 𝒇 = 𝟐 𝒍 𝝀 𝟑 = 𝟐 𝟑 𝒍 𝝀 𝟐 = 𝒍 Waves 𝝀f : fundamental frequency l : length of string or pipe 𝝀3: wavelength of third harmonic 𝝀2: wavelength of second harmonic Standing Waves on Fixed Ends String and Open Ends Pipe Standing Waves in a Closed End Pipe (Even harmonics do not exist) 𝝀 𝒇 = 𝟒 𝒍 𝝀f : fundamental wavelength l: length of pipe 𝝀 𝟑 = 𝟒 𝟑 𝒍 𝝀3: wavelength of third harmonic
12.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Waves Double Slit Light Interference 𝒏𝝀 = 𝒅. 𝒙 𝒍 𝝀: wavelength of light x: distance from the central fringe to the nth fringe l: distance from the slits to the screen 𝒅 = 𝟏 𝑵 d: distance between the slits N: number of slits per metre Diffraction Grating Light Interference 𝒅 sin 𝜽 = 𝒏 n: order of the bright fringe θ: angle between the zero order and the nth order
13.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com 𝑸 = 𝑰 𝒕 𝑽 = 𝑰 𝑹 𝑷 = 𝑽 𝑰= 𝑰 𝟐 𝑹 𝑬 = 𝑷 𝒕 Electricity Q: charge, I: current, t: time V: volts, R: resistance P: power E: energy Kirchchoff’s Laws ∑𝑰 = 𝟎 ∑𝑰: total current entering and leaving a junction ∑𝑬 = ∑𝑽 ∑E: total electro motive force around a closed loop ∑V: total potential difference around a closed loop
14.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Electricity 𝟏 𝑹 𝒑 = 𝟏 𝑹 𝟏 + 𝟏 𝑹 𝟐 𝑹 𝒑: total parallel resistance DC Circuits 𝑹 𝒔 = 𝑹 𝟏 + 𝑹 𝟐 𝑹 𝒔: total series resistance 𝑹 𝟏, 𝑹 𝟐: resistors in series 𝒁 = 𝑽 𝑰 𝒁 = 𝑿 𝑳 − 𝑿 𝑪 𝟐 + 𝑹 𝟐 Z: impedance V: RMS voltage, I: current 𝑿 𝑳: inductive reactance 𝑿 𝑪: capacitative reactance R: resistance AC Circuits 𝑷 = 𝑽𝑰 cos 𝝋 P: power cos 𝝋: power factor
15.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Electricity Resistance 𝑹 = 𝝆 𝒍 𝑨 R: resistance 𝝆 : specific resistivity l: length of conductor A: area of conductor 𝑰 = 𝒏 𝒆 𝒗 𝑨 𝑰: current 𝒏: number of free electrons/unit volume e: charge of an electron, v: drift velocity A: area of cross-section of conductor Electron Drift Velocity
16.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Electrostatics Capacitors 𝑬 𝒇 = 𝑽 𝒅 = 𝑭 𝒒 𝑪 = 𝑸 𝑽 𝑪 = 𝜺 𝟎 𝜺 𝒓 𝑨 𝒅 𝑬 𝒑 = 𝟏 𝟐 𝑪𝑽 𝟐 𝑬 𝒇: electric field strength 𝑽: voltage across charged plates 𝒅: distance between charged plates F: force, q: charge 𝑪: capacitance 𝑸: electric charge, 𝑽: voltage 𝜺 𝟎: permitivity of free space 𝜺 𝒓: relative permitivity A: area of the capacitor plate 𝑬 𝒑: electric potential energy
17.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Electrostatics Capacitor Circuits 𝟏 𝑪 𝒕 = 𝟏 𝑪 𝟏 + 𝟏 𝑪 𝟐 𝝉 = 𝑹 𝑪 𝑪 𝒕 = 𝑪 𝟏 + 𝑪 𝟐 𝑿 𝒄 = 𝟏 𝟐𝝅𝒇𝑪 𝑪 𝒕: total capacitance of series capacitors 𝑪 𝟏, 𝑪 𝟐: capacitance of capacitors 𝝉: time for voltage/current to change by 63% 𝑹: resistance in the capacitor circuit C: capacitance 𝑪 𝒕: total capacitance of parallel capacitors 𝑪 𝟏, 𝑪 𝟐: capacitance of capacitors Xc : capacitive reactance C: capacitance , f: frequency
18.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Electromagnetism 𝒗 = ∆𝝋 ∆𝒕 v: induced voltage ∆𝝋: change in flux ∆t: change in time Faraday’s Law 𝝋 = 𝑩. 𝑨 𝑿𝒍 = 𝟐𝝅𝒇𝑳 𝑩 = 𝒌 𝑰 𝒅 𝑭 = 𝑩 𝒒 𝒗 𝝋 : magnetic flux B: flux density, A: area Xl : inductive reactance , L: inductance B: flux density, k: constant d: distance from conductor F: force, v: velocity q: charge of particle
19.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com 𝑩 = 𝝁 𝟎 𝒏 𝑰 𝑬 𝒑 = 𝟏 𝟐 𝑳 𝑰 𝟐 𝑽 = −𝑳 ∆𝑰 ∆𝒕 𝝉 = 𝑳 𝑹 Electromagnetism B: flux density, 𝝁 𝟎: permeability n: number of turns, I: current 𝑬 𝒑: potential energy L: inductance V: induced volutage ∆I: change in current ∆t: cahnge in time 𝛕: time constant R: circuit resistance Inductors
20.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com 𝒗 𝒔 = −𝑴 ∆𝑰 𝒑 ∆𝒕 𝒗 𝒔 𝒗 𝒑 = 𝒏 𝒔 𝒏 𝒑 𝒏 𝒑 𝑰 𝒑 = 𝒏 𝒔 𝑰 𝒔 𝑾 𝒑 = 𝑾 𝒔 + 𝑾𝒍 Electromagnetism 𝒗 𝒔: induced secondary voltage 𝑴: mutual inductance 𝑰 𝒑: primary current ∆t: change in time 𝒗 𝒔: induced primary voltage 𝒏 𝒑: primary turns 𝒏 𝒔: secondary turns 𝑰 𝒔: secondary current 𝑾 𝒑: primary input power 𝑾 𝒔: secondary output power 𝑾𝒍: power loss Transformers
21.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Quantum Physics 𝒄 = 𝒇𝝀 𝑬 = 𝒉𝒇 𝒄: velocity of light 𝒇: frequency of light 𝝀: wavelength of light 𝑬: photon energy h: Planck’s constant 𝑬 𝒌 = 𝒉𝒇 − 𝝓 𝑬 𝒌: maximum kinetic energy of electron ϕ: work function of metal Photoelectric Effect Rydberg’s formula for Atomic Spectrum 𝟏 𝝀 = 𝑹 𝟏 𝑺 𝟐 − 𝟏 𝑳 𝟐 R: Rydberg’s constant S: Spectrum number, 1, 2, or 3 L: Spectrum Line number, L > S+1
22.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Quantum Physics Bohr’s Hydrogen Atom Model 𝑬 𝒏 = −𝒉𝒄𝑹 𝒏 𝟐 𝑬 𝒏: energy of nth state 𝒉: Planck′s constant 𝒄: velocity of light 𝑹: Rydberg′s constant 𝒏: quantum number 𝑳 = 𝒏 𝒉 𝟐𝝅 𝑳: electron angular momentum 𝒏: quantum number
23.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Nuclear Physics 𝑬 = 𝒎𝒄 𝟐 𝑬: energy 𝒎: mass 𝒄: velocity of light Einstein’s Equation Conservation Laws in Nuclear Reactions In a nuclear reaction: 1. the number of protons and neutrons is unchanged 2. the charge of nucleus remains unchanged 3. the total linear momentum or angular momentum remains unchanged
24.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Nuclear Physics Nuclear Decay 𝑻 𝟏 𝟐 = ln 𝟐 𝝀 𝑨 = 𝝀 𝑵 𝑵 = 𝑵 𝟎 𝒆−𝝀𝒕 𝑻 𝟏 𝟐 : half life 𝝀: decay constant 𝑨: activity N : number of atoms 𝑵 𝟎: number of atoms at t=0 N : number of atoms at time t
25.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Constants Name Symbol Value Acceleration due to gravity g 9.8 ms-2 Radius of Earth RE 6.37 x 106 m Universal Gravitational Constant G 6.67 x 10-11 N m2 kg-2 Coulomb’s Law Constant kc 9 x 109 Nm2C2 Mass of Electron me 9 x 10-31 kg Charge of an Electron e 1.6 x 10-19 C Magnetic Field Constant km 2 x 10-7 NA-2 Permeability of Free Space μ 1.26 x 10-6 T m A-1
26.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Constants Name Symbol Value Permittivity of Free Space ε 8.84 x 10-12 F m-1 Molar Gas Constant R 8.31 J mol-1 K-1 Velocity of Sound in Air v 332 m s-1 Velocity of Light in Space c 3 x 108 m s-1 Planck’s Constant h 6.63 x 10-34 J s Rydberg’s Constant R 1.097 x 107 m-1 Atomic Mass Unit u 1.660 x 10-27 kg Electron Volt eV 1.602 x 10-19 J
27.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Constants Parameter Symbol S I Units Dimension Units Wavelength λ metre M0 L m Frequency f Hertz M0 L0 S-1 Hz Flux Density B Tesla M L0 T2 A-1 B Electric Potential V Volt M L2 T-3 A-1 V Resistance R Ohm M L2 T-3 A-2 Ω Inductance L Henry M L2 T-2 A-2 H Capacitance C Farad M L-2 T-4 A2 F Specific Heat c - M0 L2 T-2 K-1 -
28.
FORMULAE FOR STUDENTS PHYSICS Copyright©2014, MDR,
www.learningforknowledge.com Author: M. D. Raghu glg@learningforknowledge.com Ganit Learning Guides Thank you Design and Layout: www.narayanasoftware.com www.learningforknowledge.com
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