Physics Formulae

Physics Formulae
for School Students
M. D. Raghu

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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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
Ep : elastic potential energy
k: spring constant, x: extension
f: frequency
T: time period

FORMULAE
FOR STUDENTS
PHYSICS
⍺ =
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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
h: height of liquid
𝐔𝐭 : upward thrust
𝐦 𝐝: mass of fluid displaced
𝐃 : density
𝐦: mass, V: volume

FORMULAE
FOR STUDENTS
PHYSICS
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)

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
Quantum Physics
Bohr’s Hydrogen Atom Model
𝑬 𝒏 =
−𝒉𝒄𝑹
𝒏 𝟐
𝑬 𝒏: energy of nth state
𝒉: Planck′s constant
𝑹: Rydberg′s constant
𝒏: quantum number
𝑳 =
𝒏 𝒉
𝟐𝝅
𝑳: electron angular momentum
𝒏: quantum number

FORMULAE
FOR STUDENTS
PHYSICS
Nuclear Physics
𝑬 = 𝒎𝒄 𝟐 𝑬: energy
𝒎: mass
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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

FORMULAE
FOR STUDENTS
PHYSICS
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 -

FORMULAE
FOR STUDENTS
PHYSICS
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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