Physics Formulae
for School Students
M. D. Raghu
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
๐ =๐
๐
๐ =โ๐
โ๐
๐ = ๐๐๐ +๐
๐๐๐๐
๐๐๐ = ๐๐
๐ + ๐๐๐
๐๐ = ๐๐+ ๐๐
Kinematics
v: velocity
d: distance
t: time
a: acceleration
vi : initial velocity
vf : final velocity
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Mechanics
๐ญ = ๐ ๐
ะข = ๐ญ ๐
๐ญ = โ๐ ๐
๐ฌ๐ =๐
๐๐ ๐๐
๐ฌ๐ = ๐๐ ๐
๐ญ = ๐ฎ๐๐๐๐
๐ ๐
๐ฌ๐ = โ๐ฎ๐๐๐๐
๐
F: force , m: mass
a: acceleration
ะข: 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
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Simple Harmonic Motion
๐ป = ๐๐ ๐
๐
๐ = ๐๐ ๐
๐ฌ๐ =๐
๐๐ ๐๐
๐๐๐๐ =๐๐ ๐จ
๐ป
๐ป = ๐๐ ๐
๐
๐ =๐
๐ป
m: suspended mass
๐: 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
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
โบ =๐๐
๐
ัก = ๐๐ ๐
๐ = ๐ ัก
ัก๐๐ = ัก๐
๐ + ๐ โบ ๐ฝ
๐ = ๐ ๐ฝ
ัก๐ = ัก๐ + โบ๐
๐ฝ = ัก๐t +๐
๐โบ ๐๐
Circular Motion
โบ: angular acceleration
v: linear velocity , r: radius
ัก: angular velocity
f: frequency
s: linear displacement
ัก๐ข : initial angular velocity
ัก๐ : final angular velocity
ฮ: angular displacement
t: time
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Heat
๐ฌ๐ = ๐ ๐ โ๐ป
๐ฌ๐ณ = ๐ ๐ณ๐๐: latent heat
L: specific latent heat
๐๐ก : heat energy, m: mass
c: specific heat capacity
โ๐ป: temperature difference
๐ฉ๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐ ๐ณ๐๐๐ผ๐ ๐๐๐๐ฆ ๐ด ๐๐๐ ๐๐๐๐ฆ ๐ต ๐๐๐ ๐๐ ๐กโ๐๐๐๐๐ ๐๐๐ข๐๐๐๐๐๐๐ข๐ ๐ค๐๐กโ ๐๐๐๐ฆ ๐ถ,
๐กโ๐๐ ๐ด ๐๐๐ ๐ต ๐๐๐ ๐๐ ๐๐๐ข๐๐๐๐๐๐๐ข๐ ๐ค๐๐กโ ๐๐๐โ ๐๐กโ๐๐
๐ญ๐๐๐๐ ๐๐๐๐ธ = โ๐ผ โ๐พ
Thermodynamics
๐: heat energy supplied
โU: gain in internal energy
W: work done on the system
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Heat
๐ท๐๐ฝ๐ = ๐ท๐๐ฝ๐
๐๐ : initial pressure
๐๐ : final pressure
๐๐ : initial volume
๐๐ : final volume
Boyleโs Law
๐ฝ๐๐ป๐
=๐ฝ๐๐ป๐
๐๐ : initial temperature
๐๐ : final temperature
Charleโs Law
๐ท๐๐ฝ๐๐ป๐
=๐ท๐๐ฝ๐๐ป๐
Ideal Gas Equation
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Fluid Mechanics
๐ท =๐ญ
๐จ
๐ท๐ฏ = ๐ ๐ ๐
๐ผ๐ = ๐๐ ๐
๐ซ =๐
๐ฝ
P: pressure
F: force, A: area
๐๐ : hydrostatic pressure
๐: liquid density
g: acceleration due to gravity
h: height of liquid
๐๐ญ : upward thrust
๐ฆ๐: mass of fluid displaced
๐ : density
๐ฆ: mass, V: volume
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
๐
๐=
๐
๐+๐
๐
๐ด =๐๐๐๐
๐ =๐๐๐๐
๐ =๐
๐
๐๐ ๐๐๐๐ฝ๐ = ๐๐ ๐๐๐๐ฝ๐
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
๐ฏ๐ข/๐ฏ๐ซ : angle of incidence/refraction
f: frequency , ๐: wavelength
c: velocity of light (wave)
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
๐๐ = ๐๐ โ ๐๐
๐ =๐
๐ป
๐ = ๐๐
Waves
fb : beat frequency
f1 : frequency of first wave
f2 : frequency of second wave
f: frequency
T : time period
v: wave velocity
๐: wavelength
๐โฒ = ๐๐๐
๐๐ยฑ๐๐
f โ : apparent frequency
f: source frequency
vw : wave velocity, vs : source velocity
Doppler Effect
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
๐ ๐ = ๐ ๐
๐๐ =๐
๐๐
๐๐ = ๐
Waves
๐f : fundamental frequency
l : length of string or pipe
๐3: wavelength of third harmonic
๐2: 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)
๐๐ = ๐ ๐ ๐f : fundamental wavelength
l: length of pipe
๐๐ =๐
๐๐ ๐3: wavelength of third harmonic
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Waves
Double Slit Light Interference
๐๐ =๐ . ๐
๐
๐: wavelength of light
x: distance from the central fringe to
the nth fringe
l: distance from the slits to the screen
๐ =๐
๐ต
d: distance between the slits
N: number of slits per metre
Diffraction Grating Light Interference
๐ sin๐ฝ = ๐n: order of the bright fringe
ฮธ: angle between the zero
order and the nth order
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
๐ธ = ๐ฐ ๐
๐ฝ = ๐ฐ ๐น
๐ท = ๐ฝ ๐ฐ= ๐ฐ๐ ๐น
๐ฌ = ๐ท ๐
Electricity
Q: charge, I: current, t: time
V: volts, R: resistance
P: power
E: energy
Kirchchoffโs Laws
โ๐ฐ = ๐โ๐ฐ: total current entering and
leaving a junction
โ๐ฌ = โ๐ฝ
โE: total electro motive force
around a closed loop
โV: total potential difference
around a closed loop
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Electricity
๐
๐น๐=
๐
๐น๐+
๐
๐น๐
๐น๐: total parallel resistance
DC Circuits
๐น๐ = ๐น๐ + ๐น๐๐น๐: total series resistance
๐น๐, ๐น๐: resistors in series
๐ =๐ฝ
๐ฐ
๐ = ๐ฟ๐ณ โ ๐ฟ๐ช๐ + ๐น๐
Z: impedance
V: RMS voltage, I: current
๐ฟ๐ณ: inductive reactance
๐ฟ๐ช: capacitative reactance
R: resistance
AC Circuits
๐ท = ๐ฝ๐ฐ cos๐ P: power
cos๐: power factor
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Electricity
Resistance
๐น =๐ ๐
๐จ
R: resistance
๐ : specific resistivity
l: length of conductor
A: area of conductor
๐ฐ = ๐ ๐ ๐ ๐จ๐ฐ: current
๐: number of free electrons/unit volume
e: charge of an electron, v: drift velocity
A: area of cross-section of conductor
Electron Drift Velocity
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Electrostatics
Capacitors
๐ฌ๐ =๐ฝ
๐ =๐ญ
๐
๐ช =๐ธ
๐ฝ
๐ช =๐บ๐๐บ๐๐จ
๐
๐ฌ๐ =๐
๐๐ช๐ฝ๐
๐ฌ๐: electric field strength
๐ฝ: voltage across charged plates
๐ : distance between charged plates
F: force, q: charge
๐ช: capacitance
๐ธ: electric charge, ๐ฝ: voltage
๐บ๐: permitivity of free space
๐บ๐: relative permitivity
A: area of the capacitor plate
๐ฌ๐: electric potential energy
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Electrostatics
Capacitor Circuits
๐
๐ช๐=
๐
๐ช๐+
๐
๐ช๐
๐ = ๐น ๐ช
๐ช๐ = ๐ช๐ + ๐ช๐
๐ฟ๐ =๐
๐๐ ๐๐ช
๐ช๐: total capacitance of series capacitors
๐ช๐, ๐ช๐: capacitance of capacitors
๐: time for voltage/current to change by 63%
๐น: resistance in the capacitor circuit
C: capacitance
๐ช๐: total capacitance of parallel capacitors
๐ช๐, ๐ช๐: capacitance of capacitors
Xc : capacitive reactance
C: capacitance , f: frequency
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Electromagnetism
๐ =โ๐
โ๐
v: induced voltage
โ๐: change in flux
โt: change in time
Faradayโs Law
๐ = ๐ฉ.๐จ
๐ฟ๐ = ๐๐ ๐๐ณ
๐ฉ = ๐๐ฐ
๐
๐ญ = ๐ฉ ๐ ๐
๐ : 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
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
๐ฉ = ๐๐ ๐ ๐ฐ
๐ฌ๐ =๐
๐๐ณ ๐ฐ๐
๐ฝ = โ๐ณโ๐ฐ
โ๐
๐ =๐ณ
๐น
Electromagnetism
B: flux density, ๐๐: permeability
n: number of turns, I: current
๐ฌ๐: potential energy
L: inductance
V: induced volutage
โI: change in current
โt: cahnge in time
๐: time constant
R: circuit resistance
Inductors
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
๐๐ = โ๐ดโ๐ฐ๐
โ๐
๐๐๐๐
=๐๐๐๐
๐๐๐ฐ๐ = ๐๐๐ฐ๐
๐พ๐ = ๐พ๐ +๐พ๐
Electromagnetism
๐๐: induced secondary voltage
๐ด: mutual inductance
๐ฐ๐: primary current
โt: change in time
๐๐: induced primary voltage
๐๐: primary turns
๐๐: secondary turns
๐ฐ๐: secondary current
๐พ๐: primary input power
๐พ๐: secondary output power
๐พ๐: power loss
Transformers
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Quantum Physics
๐ = ๐๐
๐ฌ = ๐๐
๐: velocity of light
๐: frequency of light
๐: wavelength of light
๐ฌ: photon energy
h: Planckโs constant
๐ฌ๐ = ๐๐ โ ๐ ๐ฌ๐: maximum kinetic energy
of electron
ฯ: work function of metal
Photoelectric Effect
Rydbergโs formula for Atomic Spectrum
๐
๐= ๐น
๐
๐บ๐โ๐
๐ณ๐
R: Rydbergโs constant
S: Spectrum number, 1, 2, or 3
L: Spectrum Line number, L > S+1
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Quantum Physics
Bohrโs Hydrogen Atom Model
๐ฌ๐ =โ๐๐๐น
๐๐
๐ฌ๐: energy of nth state
๐: Planckโฒs constant
๐: velocity of light
๐น: Rydbergโฒs constant
๐: quantum number
๐ณ =๐ ๐
๐๐
๐ณ: electron angular momentum
๐: quantum number
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Nuclear Physics
๐ฌ = ๐๐๐ ๐ฌ: energy
๐: mass
๐: velocity of light
Einsteinโs 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
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Nuclear Physics
Nuclear Decay
๐ป๐๐
=ln๐
๐
๐จ = ๐ ๐ต
๐ต = ๐ต๐๐โ๐๐
๐ป๐๐: half life
๐: decay constant
๐จ: activity
N : number of atoms
๐ต๐: number of atoms at t=0
N : number of atoms at time t
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, 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
Coulombโs 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 ฮผ 1.26 x 10-6 T m A-1
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Constants
Name Symbol Value
Permittivity of Free Space ฮต 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
Planckโs Constant h 6.63 x 10-34 J s
Rydbergโs 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
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Constants
Parameter Symbol S I Units Dimension Units
Wavelength ฮป 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 ฮฉ
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 -
FORMULAE
FOR STUDENTSPHYSICS
Copyrightยฉ2014, MDR, www.learningforknowledge.com
Author: M. D. Raghu
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