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COMPLETE FORMULAS IN GENERAL PHYSICS

VARUN RAJ

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29 May 2008 11:14:11 IST

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29 May 2008 11:14:11 IST

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COMPLETE FORMULAS IN GENERAL PHYSICS

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ALL THE FORMULAS IN PHYSICS LEAVING MODERN PHYSICS

Position vector
Instantaneous velocity
Instantaneous acceleration
Constant linear acceleration
Range
Angular velocity
Angular acceleration
Period
Frequency
Circumferential velocity
Centripetal acceleration
Newton’s 2^nd Law
Force of a spring (Hooke's Law)
Force of friction		static friction kinetic friction
Universal Law of Gravitation
Linear momentum
Newton’s second law of motion
Impulse
Linear momentum of a system of particles		for i particles
Kinetic energy of a particle
Work and Work-Energy theorem
Power
Potential energy of a spring		k is the spring constant
Gravitational potential energy near the surface of a planet		y << radius of the planet
Gravitational potential energy at any distance from a planet		M is the mass of the planet
Total mechanical energy of a system of particles		for i particles
Angular momentum
Angular momentum of a rotating particle
Torque
Rate of change of angular momentum
Power on a rotating system
Center of mass		for j particles
One dimensional elastic collision of two particles		where m₁ and m₂are the masses of particles one and two, v₁ and v₂ are their initial speeds, and u₁and u₂ are their final speeds
Angular velocity of a rigid body
Angular acceleration of a rigid body
Rotational kinematics with constant acceleration
Rolling without slipping
Kinetic energy of a rotating rigid body
Moment of rotational inertia
Dynamic relations for rigid bodies with rotational or mirror symmetry		subscript A refers to a given axis
Density
Pressure
Pressure in an ideal gas		for an incompressible liquid: r = constant
Pressure gradient of a static fluid in a gravitational field
Archimedes’ principle
Equation of motion for a spring and any simple harmonic oscillator
Angular frequency for an oscillating spring
Displacement and velocity of an oscillating spring		two alternative expressions. x and A are replaced by q andq_max for a simple pendulum
Angular frequency of a simple pendulum
Total energy in an oscillating spring
Total energy in a simple pendulum

Angular frequency		f = frequency T = period
Speed of any wave
Relation between wavelength and the propagation constant
Displacement function for a wave on a string		A = amplitude = phase angle moving right moving left
Speed of a wave on a string		T = tension m = mass/length
Average power transmitted by a wave on a string
Displacement function for a standing wave
Allowed wavelengths for standing waves with displacement nodes at each end		n = 1, 2, 3, . . . L = length of string or pipe
Allowed wavelengths for standing waves with a displacement node at one end and an antinode at the other		m = 1, 2, 3, . . .
Description of a one-dimensional sound wave		Displacement velocity density pressure
Speed of sound		γ = ratio of specific heats P = pressure ρ = density

Pressure amplitude of a sound wave		k = Boltzmann’s constant P₀ = ambient pressure
Index of refraction		Where c is the velocity of light in a vacuum and v is the velocity of light in the medium
Intensity of a sound wave
Sound intensity level		dB is decibels I in W/m²
Inverse square law for intensity		where r₁ and r₂ are two different radii from a point source
Doppler effect for sound		= wave velocity = observer velocity relative to air = source velocity relative to air
Doppler effect for light		v_radial << c
Relativistic Doppler effect for light		for a blueshift Change the sign of v_radial for a redshift
Law of reflection
Snell’s law
Superposition of Two Harmonic Wave Functions		Δφ = phase difference between the two harmonic wave functions
Maxima for 2 Slit Interference		d = separation between slits θ = angle from the center line m = 0, 1, 2, . . .
Minima for 2 Slit Interference		m = 0, 1, 2, . . .
Diffraction Minima for Rectangular Slit		a = slit width θ = angle from the center line m = 0, 1, 2, . . .
First Diffraction Minimum for a Circular Aperture		a = aperture diameter θ = angle from the center line
Image in a Plane Mirror		= image distance = object distance
Image Formed by Plane Refracting Surfaces		= index of refraction of the medium where the object is = index of refraction of the medium from which the object is observed
Image Formed by a Spherical Mirror		f = focal length r = radius of the spherical mirror
Lens Maker’s Equation		= radius of the front surface = radius of the back surface n = index of refraction of the lens material = index of refraction of the outside medium
Image Formed by a Thin Lens
Magnification of an Image		= height of the object = height of the image

Temperature Conversion

T(°C) = 5/9 [T(°F) – 32°F]

T(°F) = 9/5 T(°C) + 32°F

T(K) = T(°C) + 273.15 K

T = temperature

Boyle’s Law for a gas

T = constant

P = pressure

V = volume

Charles’ Law for a gas

P = constant

Ideal Gas Law

N = number of molecules

N_mol = number of moles

k = 1.38066 x 10^-23 J/K Boltzmann’s constant

R = kN_A = 8.3145 J/(mol K) ideal gas constant

Translational kinetic energy K per gas molecule

Root mean square speed of a gas molecule

m = molecular mass

Internal energy U of a monatomic ideal gas

First Law of Thermodynamics

Q = heat added to system

W = work done by system

Work done by an ideal gas

Specific heat c for a given process

M = Nm = total mass

Specific heat c_V of a monatomic ideal gas at constant volume

Specific heat c_P of a monatomic ideal gas at constant pressure

Ratio of specific heats γ

Relation between c_P andc_V for an ideal gas

Adiabatic gas law

ΔQ = 0

Work done by a monatomic ideal gas in an adiabatic process

Latent heat of fusion

where Q_L and Q_S are measured at the freezing point

Latent heat of vaporization

where Q_V and Q_L are measured at the boiling point

Linear expansion

where α is the coefficient of linear thermal expansion

Volume expansion

where β is the coefficient of volume expansion

Heat Capacity C

Heat transfer H along a rod

k = thermal conductivity

A = cross-sectional area

? = rod length

Thermal resistance Rand R-factor R_f

Wien’s displacement law

λ_maxT = 2.898 x 10^-3 K m

Power radiated

L = luminosity

σ = 5.67 x 10^-8 W/m² K⁴Stefan-Boltzmann constant

ε = emissivity

Efficiency e of a heat engine

Efficiency of a reversible heat engine (Carnot cycle)

T_C = cold temperature

T_H = hot temperature

Entropy change ΔS

Ratio relation for a reversible engine

Coulomb’s Law		Q = electric charge r₂₁ = distance from Q₁ toQ₂ k = 8.99 x 10⁹ N m²/C²
Permittivity of free space ε₀		ε₀ = 8.85 x 10^-12 C²/N m²
Electric Field		where is the force experienced by a test chargeq
Electric Field of a point charge Q₁
Superposition of electric fields from many point charges
Electric flux Φ_E through a closed surface		element of surface area directed normal to the surface
Gauss’ Law		1^st Maxwell Equation
Uniform charge distributions for filaments, surfaces, and volumes		where λ is the linear charge density, σ is the surface charge density, and ρ is the volume charge density
Acceleration of a charged particle of massm and charge q in an electric field
Dipole moment p of an electric dipole		where the length is directed from –Q to +Q
Torque on an electric dipole in an electric field
Work to move a test charge q from r₁ to r₂ in the electric field of a point charge Q

Potential energy of a test charge q in the presence of a point charge Q
Work to move a test charge q from P₁ to P₂in an arbitrary electric field
Change in potential energy to move a test charge q from P₁ to P₂in an arbitrary electric field
Electric potential difference
Electric potential at r of a point charge Qreferenced from ∞
Electric potential at Pof a system of N point charges
Potential energy of an arbitrary system of point charges Q_i
Electric potential at a perpendicular distancea from an infinite, uniformly charged wire with a linear charge density λ		r₀ is the reference distance where V(r₀) = 0
Electric field of a conducting surface with charge density σ
Electric current I
Ohm’s Law
Ohmic loss or Joule heating
Current density		where A is the cross-sectional area, n_e is the free electron density, is the electron drift velocity, τ is the mean time between collisions,m_e is the mass of the electron and σ is the conductivity
Conductivity σ
Resistivity ρ
Ohm’s Law
Resistance of a wire of cross-sectional area Aand length ?
Temperature dependence of resistivity for most conductors		where ρ₀ is the resistivity at a reference temperatureT₀ and α is the temperature coefficient
Resistors in series
Resistors in parallel
Kirchhoff’s junction rule
Kirchhoff’s loop rule
Capacitance C
Capacitance C of a parallel plate capacitor of surface area A, plate separation d, and dielectric constant κ
Stored energy U in a capacitor
Capacitors in parallel
Capacitors in series
Dielectric constant κ		where E_a is the applied electric field and E is the net electric field
Energy density in an electric field
Magnetic force law
Biot-Savart law		where N/A²is the permeability of free-space, r is the displacement from d? to P and I is the current in the direction of d?
Magnetic induction on the axis of a current Iin a circular loop of radius a		determine using the right hand rule
Magnetic dipole moment of a current loop		m is a vector with direction given by the right hand rule, A is the cross-sectional area
Gauss’s Law for Magnetic Fields		2^nd Maxwell Equation
Ampère’s Law
Magnetic induction from a current I in a long straight wire		r is the perpendicular distance from the wire
Magnetic induction in a solenoid		where n is the number of turns/unit length and is along the axis of the solenoid as given by the right hand rule
Motion perpendicular to a uniform magnetic field B		where m, v, and q are respectively the mass, speed, and charge of the particle, r_L is the Larmor radius, and ω_C is the cyclotron frequency
Lorentz force law
Force on a current-carrying wire
Torque on a current loop in a magnetic fieldB		where m is the magnetic moment of the current loop
Faraday’s Law (the – sign in the last two terms is the result of Lenz’s law)		3^rd Maxwell Equation
Induced electromotive force
Electromotive force of a generator rotating at an angular speed ω		where N is the number of turns in the generator coil,B is the uniform magnetic induction across the coil and A is the cross-sectional area of the coil
Torque of a simple electric motor		where N is the number of turns in the motor coil, Bis the uniform magnetic induction across the coil,A is the cross-sectional area of the coil, I is the current and θ is the angle between the normal of the coil and the magnetic induction
Electromotive force driving a simple electric motor		where r is the resistance of the motor and the other symbols are as above
Displacement currentI_d
Ampère-Maxwell Law		4^th Maxwell Equation
RC Circuit (discharging)		where τ_C is the time constant
RC Circuit (charging)
Self-Inductance L
Self-Inductance of a Solenoid		where N is the number of turns, ? the length, n the number of turns per unit length and A the cross-sectional area of the solenoid
Energy stored in an Inductor
Energy density in a magnetic field
Energy density in an electromagnetic field
Mutual Inductance M		where 1 refers to one circuit and 2 to another conjoined only by mutual inductance
Relationship of electromotive force to the number of turns Nin a transformer		where s refers to the secondary coil and p to the primary coil
LR Circuit (decaying)		where τ_L is the time constant
LR Circuit (increasing)
LC Circuit
LRC Circuit
Alternating Current Circuits
Charge and current for a capacitor in an alternating current
Current in an inductor in an alternating current
rms potential in an alternating circuit
Average power in an alternating current circuit
Reactance of a capacitor		Phase shift of –π/2
Reactance of an inductor		Phase shift of +π/2
Impedance Z of an RC Circuit
Phase angle φ in an RC Circuit
Impedance Z of an LR Circuit
Phase angle φ in an LR Circuit
Impedance Z of an LRC Circuit
Phase angle φ in an LRC Circuit
Current I in RC, LR and LRC Circuits		Voltage is given by
Average power in RC, LR and LRC Circuits
Natural or resonance frequency of an LRC Circuit
Voltage amplification across the capacitor in an LRC circuit at the resonance frequency

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Comments (4)

VARUN RAJ

Blazing goIITian

Joined: 16 Mar 2008 12:29:41 IST

Posts: 1825

29 May 2008 12:11:54 IST

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PLS COMMENT

Abhishek Varshney

Scorching goIITian

Joined: 8 Apr 2007 16:13:57 IST

Posts: 247

29 May 2008 13:06:59 IST

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nice work

VARUN RAJ

Blazing goIITian

Joined: 16 Mar 2008 12:29:41 IST

Posts: 1825

29 May 2008 15:59:07 IST

Like 0 people liked this

PS COMMENT

iitaspirant10

Blazing goIITian

Joined: 16 Dec 2006 14:57:10 IST

Posts: 424

29 May 2008 17:07:20 IST

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tan Q...where did u get it from?lot of it is missing

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ALL THE FORMULAS IN PHYSICS LEAVING MODERN PHYSICS

Position vector

Instantaneous velocity

Instantaneous acceleration

Constant linear acceleration

Range

Angular velocity

Angular acceleration

Period

Frequency

Circumferential velocity

Centripetal acceleration

Newton’s 2nd Law

Force of a spring (Hooke's Law)

Force of friction

static friction kinetic friction

Universal Law of Gravitation

Linear momentum

Newton’s second law of motion

Impulse

Linear momentum of a system of particles

for i particles

Kinetic energy of a particle

Work and Work-Energy theorem

Power

Potential energy of a spring

k is the spring constant

Gravitational potential energy near the surface of a planet

y << radius of the planet

Gravitational potential energy at any distance from a planet

M is the mass of the planet

Total mechanical energy of a system of particles

for i particles

Angular momentum

Angular momentum of a rotating particle

Torque

Rate of change of angular momentum

Power on a rotating system

Center of mass

for j particles

One dimensional elastic collision of two particles

where m1 and m2are the masses of particles one and two, v1 and v2 are their initial speeds, and u1and u2 are their final speeds

Angular velocity of a rigid body

Angular acceleration of a rigid body

Rotational kinematics with constant acceleration

Rolling without slipping

Kinetic energy of a rotating rigid body

Moment of rotational inertia

Dynamic relations for rigid bodies with rotational or mirror symmetry

subscript A refers to a given axis

Density

Pressure

Pressure in an ideal gas

for an incompressible liquid: r = constant

Pressure gradient of a static fluid in a gravitational field

Archimedes’ principle

Equation of motion for a spring and any simple harmonic oscillator

Angular frequency for an oscillating spring

Displacement and velocity of an oscillating spring

two alternative expressions. x and A are replaced by q andqmax for a simple pendulum

Angular frequency of a simple pendulum

Total energy in an oscillating spring

Newton’s 2^nd Law

static friction

kinetic friction

where m₁ and m₂are the masses of particles one and two, v₁ and v₂ are their initial speeds, and u₁and u₂ are their final speeds

two alternative expressions.

x and A are replaced by q andq_max for a simple pendulum