Physics Formulae
-
Upload
dhatiraghu -
Category
Education
-
view
631 -
download
9
description
Transcript of 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
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
g: acceleration due to gravity
Ep : elastic potential energy
k: spring constant, x: extension
f: frequency
T: time period
FORMULAE
FOR STUDENTSPHYSICS
Copyright©2014, MDR, www.learningforknowledge.com
⍺ =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
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
g: acceleration due to gravity
h: height of liquid
𝐔𝐭 : upward thrust
𝐦𝐝: mass of fluid displaced
𝐃 : density
𝐦: mass, V: volume
FORMULAE
FOR STUDENTSPHYSICS
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
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 sin𝜽 = 𝒏n: order of the bright fringe
θ: angle between the zero
order and the nth order
FORMULAE
FOR STUDENTSPHYSICS
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
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 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
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
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 = 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
Copyright©2014, MDR, www.learningforknowledge.com
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
Copyright©2014, MDR, www.learningforknowledge.com
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
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
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
Copyright©2014, MDR, www.learningforknowledge.com
Quantum Physics
Bohr’s Hydrogen Atom Model
𝑬𝒏 =−𝒉𝒄𝑹
𝒏𝟐
𝑬𝒏: 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
FORMULAE
FOR STUDENTSPHYSICS
Copyright©2014, MDR, www.learningforknowledge.com
Nuclear Physics
𝑬 = 𝒎𝒄𝟐 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
FORMULAE
FOR STUDENTSPHYSICS
Copyright©2014, MDR, www.learningforknowledge.com
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
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
FORMULAE
FOR STUDENTSPHYSICS
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
FORMULAE
FOR STUDENTSPHYSICS
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 -
FORMULAE
FOR STUDENTSPHYSICS
Copyright©2014, MDR, www.learningforknowledge.com
Author: M. D. Raghu
Ganit Learning Guides
Thank you
Design and Layout: www.narayanasoftware.com
www.learningforknowledge.com