Physics Formulae

Physics Formulae

for School Students

M. D. Raghu

FORMULAE

FOR STUDENTSPHYSICS

Copyright©2014, MDR, www.learningforknowledge.com

𝒗 =𝒅

𝒕

𝒂 =∆𝒗

∆𝒕

𝒅 = 𝒗𝒊𝒕 +𝟏

𝟐𝒂𝒕𝟐

𝒗𝒇𝟐 = 𝒗𝒊

𝟐 + 𝟐𝒂𝒅

𝒗𝒇 = 𝒗𝒊+ 𝒂𝒕

Kinematics

v: velocity

d: distance

t: time

a: acceleration

vi : initial velocity

vf : final velocity

FORMULAE

FOR STUDENTSPHYSICS


Mechanics

𝑭 = 𝒎 𝒂

Т = 𝑭 𝒅

𝑭 = −𝒌 𝒙

𝑬𝒌 =𝟏

𝟐𝒎 𝒗𝟐

𝑬𝒑 = 𝒎𝒈 𝒉

𝑭 = 𝑮𝒎𝟏𝒎𝟐

𝒅𝟐

𝑬𝒑 = −𝑮𝒎𝟏𝒎𝟐

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 STUDENTSPHYSICS


Simple Harmonic Motion

𝑻 = 𝟐𝝅𝒎

𝒌

𝝎 = 𝟐𝝅𝒇

𝑬𝒑 =𝟏

𝟐𝒌 𝒙𝟐

𝒗𝒎𝒂𝒙 =𝟐𝝅𝑨

𝑻

𝑻 = 𝟐𝝅𝒍

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 STUDENTSPHYSICS


⍺ =𝒗𝟐

𝒓

ѡ = 𝟐𝝅𝒇

𝒗 = 𝒓 ѡ

ѡ𝒇𝟐 = ѡ𝒊

𝟐 + 𝟐 ⍺ 𝜽

𝒔 = 𝒓 𝜽

ѡ𝒇 = ѡ𝒊 + ⍺𝒕

𝜽 = ѡ𝒊t +𝟏

𝟐⍺ 𝒕𝟐

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 STUDENTSPHYSICS


Heat

𝑬𝒉 = 𝒎 𝒄 ∆𝑻

𝑬𝑳 = 𝒎 𝑳𝐄𝐋: latent heat

L: specific latent heat

𝐄𝐡 : heat energy, m: mass

c: specific heat capacity

∆𝑻: temperature difference

𝑩𝒂𝒔𝒊𝒄 𝒐𝒓 𝒁𝒆𝒓𝒐𝒆𝒕𝒉 𝑳𝒂𝒘𝐼𝑓 𝑏𝑜𝑑𝑦 𝐴 𝑎𝑛𝑑 𝑏𝑜𝑑𝑦 𝐵 𝑎𝑟𝑒 𝑖𝑛 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑤𝑖𝑡ℎ 𝑏𝑜𝑑𝑦 𝐶,

𝑡ℎ𝑒𝑛 𝐴 𝑎𝑛𝑑 𝐵 𝑎𝑟𝑒 𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑤𝑖𝑡ℎ 𝑒𝑎𝑐ℎ 𝑜𝑡ℎ𝑒𝑟

𝑭𝒊𝒓𝒔𝒕 𝒍𝒂𝒘𝑸 = ∆𝑼 −𝑾

Thermodynamics

𝐐: heat energy supplied

∆U: gain in internal energy

W: work done on the system

FORMULAE

FOR STUDENTSPHYSICS


Heat

𝑷𝟏𝑽𝟏 = 𝑷𝟐𝑽𝟐

𝐏𝟏 : initial pressure

𝐏𝟐 : final pressure

𝐕𝟏 : initial volume

𝐕𝟐 : final volume

Boyle’s Law

𝑽𝟏𝑻𝟏

=𝑽𝟐𝑻𝟐

𝐓𝟏 : initial temperature

𝐓𝟐 : final temperature

Charle’s Law

𝑷𝟏𝑽𝟏𝑻𝟏

=𝑷𝟐𝑽𝟐𝑻𝟐

Ideal Gas Equation

FORMULAE

FOR STUDENTSPHYSICS


Fluid Mechanics

𝑷 =𝑭

𝑨

𝑷𝑯 = 𝝆 𝒈 𝒉

𝑼𝒕 = 𝒎𝒅 𝒈

𝑫 =𝒎

𝑽

P: pressure

F: force, A: area

𝐏𝐇 : hydrostatic pressure

𝝆: liquid density


h: height of liquid

𝐔𝐭 : upward thrust

𝐦𝐝: mass of fluid displaced

𝐃 : density

𝐦: mass, V: volume

FORMULAE

FOR STUDENTSPHYSICS


𝟏

𝒇=

𝟏

𝒖+𝟏

𝒗

𝑴 =𝒉𝒊𝒉𝟎

𝒏 =𝒄𝒊𝒄𝒓

𝝀 =𝒄

𝒇

𝒏𝒊 𝒔𝒊𝒏𝜽𝒊 = 𝒏𝒓 𝒔𝒊𝒏𝜽𝒓

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/𝚯𝐫 : angle of incidence/refraction

f: frequency , 𝛌: wavelength

c: velocity of light (wave)

FORMULAE

FOR STUDENTSPHYSICS


𝒇𝒃 = 𝒇𝟏 − 𝒇𝟐

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′ = 𝒇𝒗𝒘

𝒗𝒘±𝒗𝒔

f ’ : apparent frequency

f: source frequency

vw : wave velocity, vs : source velocity

Doppler Effect

FORMULAE

FOR STUDENTSPHYSICS


𝝀 𝒇 = 𝟐 𝒍

𝝀𝟑 =𝟐

𝟑𝒍

𝝀𝟐 = 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)

𝝀𝒇 = 𝟒 𝒍 𝝀f : fundamental wavelength

l: length of pipe

𝝀𝟑 =𝟒

𝟑𝒍 𝝀3: wavelength of third harmonic

FORMULAE

FOR STUDENTSPHYSICS


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 sin𝜽 = 𝒏n: order of the bright fringe

θ: angle between the zero

order and the nth order

FORMULAE

FOR STUDENTSPHYSICS


𝑸 = 𝑰 𝒕

𝑽 = 𝑰 𝑹

𝑷 = 𝑽 𝑰= 𝑰𝟐 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 STUDENTSPHYSICS


Electricity

𝟏

𝑹𝒑=

𝟏

𝑹𝟏+

𝟏

𝑹𝟐

𝑹𝒑: total parallel resistance

DC Circuits

𝑹𝒔 = 𝑹𝟏 + 𝑹𝟐𝑹𝒔: total series resistance

𝑹𝟏, 𝑹𝟐: resistors in series

𝒁 =𝑽

𝑰

𝒁 = 𝑿𝑳 − 𝑿𝑪𝟐 + 𝑹𝟐

Z: impedance

V: RMS voltage, I: current

𝑿𝑳: inductive reactance

𝑿𝑪: capacitative reactance

R: resistance

AC Circuits

𝑷 = 𝑽𝑰 cos𝝋 P: power

cos𝝋: power factor

FORMULAE

FOR STUDENTSPHYSICS


Electricity

Resistance

𝑹 =𝝆 𝒍

𝑨

R: resistance

𝝆 : specific resistivity

l: length of conductor

A: area of conductor

𝑰 = 𝒏 𝒆 𝒗 𝑨𝑰: 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 STUDENTSPHYSICS


Electrostatics

Capacitors

𝑬𝒇 =𝑽

𝒅=𝑭

𝒒

𝑪 =𝑸

𝑽

𝑪 =𝜺𝟎𝜺𝒓𝑨

𝒅

𝑬𝒑 =𝟏

𝟐𝑪𝑽𝟐

𝑬𝒇: electric field strength

𝑽: voltage across charged plates

𝒅: distance between charged plates

F: force, q: charge

𝑪: capacitance

𝑸: electric charge, 𝑽: voltage

𝜺𝟎: permitivity of free space

𝜺𝒓: relative permitivity

A: area of the capacitor plate

𝑬𝒑: electric potential energy

FORMULAE

FOR STUDENTSPHYSICS


Electrostatics

Capacitor Circuits

𝟏

𝑪𝒕=

𝟏

𝑪𝟏+

𝟏

𝑪𝟐

𝝉 = 𝑹 𝑪

𝑪𝒕 = 𝑪𝟏 + 𝑪𝟐

𝑿𝒄 =𝟏

𝟐𝝅𝒇𝑪

𝑪𝒕: total capacitance of series capacitors

𝑪𝟏, 𝑪𝟐: capacitance of capacitors

𝝉: time for voltage/current to change by 63%

𝑹: resistance in the capacitor circuit

C: capacitance

𝑪𝒕: total capacitance of parallel capacitors

𝑪𝟏, 𝑪𝟐: capacitance of capacitors

Xc : capacitive reactance

C: capacitance , f: frequency

FORMULAE

FOR STUDENTSPHYSICS


Electromagnetism

𝒗 =∆𝝋

∆𝒕

v: induced voltage

∆𝝋: change in flux

∆t: change in time

Faraday’s Law

𝝋 = 𝑩.𝑨

𝑿𝒍 = 𝟐𝝅𝒇𝑳

𝑩 = 𝒌𝑰

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 STUDENTSPHYSICS


𝑩 = 𝝁𝟎 𝒏 𝑰

𝑬𝒑 =𝟏

𝟐𝑳 𝑰𝟐

𝑽 = −𝑳∆𝑰

∆𝒕

𝝉 =𝑳

𝑹

Electromagnetism

B: flux density, 𝝁𝟎: permeability

n: number of turns, I: current

𝑬𝒑: potential energy

L: inductance

V: induced volutage

∆I: change in current

∆t: cahnge in time

𝛕: time constant

R: circuit resistance

Inductors

FORMULAE

FOR STUDENTSPHYSICS


𝒗𝒔 = −𝑴∆𝑰𝒑

∆𝒕

𝒗𝒔𝒗𝒑

=𝒏𝒔𝒏𝒑

𝒏𝒑𝑰𝒑 = 𝒏𝒔𝑰𝒔

𝑾𝒑 = 𝑾𝒔 +𝑾𝒍

Electromagnetism

𝒗𝒔: induced secondary voltage

𝑴: mutual inductance

𝑰𝒑: primary current

∆t: change in time

𝒗𝒔: induced primary voltage

𝒏𝒑: primary turns

𝒏𝒔: secondary turns

𝑰𝒔: secondary current

𝑾𝒑: primary input power

𝑾𝒔: secondary output power

𝑾𝒍: power loss

Transformers

FORMULAE

FOR STUDENTSPHYSICS


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

𝑬𝒌 = 𝒉𝒇 − 𝝓 𝑬𝒌: maximum kinetic energy

of electron

ϕ: work function of metal

Photoelectric Effect

Rydberg’s formula for Atomic Spectrum

𝟏

𝝀= 𝑹

𝟏

𝑺𝟐−𝟏

𝑳𝟐

R: Rydberg’s constant

S: Spectrum number, 1, 2, or 3

L: Spectrum Line number, L > S+1

FORMULAE

FOR STUDENTSPHYSICS


Quantum Physics

Bohr’s Hydrogen Atom Model

𝑬𝒏 =−𝒉𝒄𝑹

𝒏𝟐

𝑬𝒏: 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 STUDENTSPHYSICS


Nuclear Physics

𝑬 = 𝒎𝒄𝟐 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 STUDENTSPHYSICS


Nuclear Physics

Nuclear Decay

𝑻𝟏𝟐

=ln𝟐

𝝀

𝑨 = 𝝀 𝑵

𝑵 = 𝑵𝟎𝒆−𝝀𝒕

𝑻𝟏𝟐: half life

𝝀: decay constant

𝑨: activity

N : number of atoms

𝑵𝟎: number of atoms at t=0

N : number of atoms at time t

FORMULAE

FOR STUDENTSPHYSICS


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 STUDENTSPHYSICS


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 STUDENTSPHYSICS


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 STUDENTSPHYSICS


Author: M. D. Raghu

[email protected]

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Physics Formulae