Physics is a fundamental branch of science that studies matter, its fundamental constituents, and its motion and behavior through space and time. Physics Formulas are very important during applications of various concepts of physics.
In this article, we will cover all important formulas related to physics ranging from mechanics to electromagnetism as well as thermodynamics and quantum mechanics.
Below is the list of all important formulas related to physics:
Physics Formulas | Formulas |
|---|
Frequency Formula | F = v/λ |
Kinetic Energy Formula | E = 1/2 mv2 |
Ohm’s Law Formula | V = I × R |
Pressure Formula | P = F/A |
Weight Formula | W = mg |
Newton’s Second Law | F = m × a |
Power Formula | P = W/t |
Density Formula | P = m/V |
Acceleration Formula | a = v - u/t |
Average Speed Formula | S = d/t |
Pendulum Formula | T = 2π√L/g |
Fahrenheit Formula | F = (9/5 × °C) + 32 |
Work Formula | W = F × d × cosθ |
Torque Formula | T = F × r × sinθ |
Displacement Formula | ΔX = Xf–Xi |
Mass Formula | F = m × a or m = F/a |
Amplitude Formula | x = A sin (ωt + ϕ) |
Tension Formula | T = mg + ma |
Surface Charge Density Formula | σ = q / A |
Linear Speed Formula | V(linear speed) = ΔS/ΔT |
Position Formula | Δx = x2 − x1 |
Heat of Fusion Formula | q = m × ΔHF |
Gravity Formula | F α m1m2/r2 |
Spring Potential Energy Formula | P.E = 1/2 k × x2 |
Physics Kinematics Formula | v2 = vo2 + 2a(x - xo) |
DC Voltage Drop Formula | V = I × R |
Hubble’s Law Formula | v = Hor |
Induced Voltage Formula | e = – N(dΦB/dt) |
Latent Heat Formula | L = Q / M |
Wavelength Formula | λ = v/f |
Gravitational Force Formula | F = G(m1m2)/R2 |
Potential Energy Formula | PE = mgh |
Strain Energy Formula | U = Fδ / 2 |
Friction Force Formula | f = μN |
Cell Potential Formula | Ecell = Ecathode − Eanode |
Shear Modulus Formula | (shear stress)/(shear strain) = (F/A)/(x/y) |
Water Pressure Formula | Water pressure = ρ g h |
Refractive Index Formula | n = c/v |
Centroid Formula | C = [(x1 + x2 + x3)/ 3, (y1 + y2 + y3)/ 3] |
Few important mechanics formulas are given below:
Newton's Second Law of Motion
F = m × a
Where:
- F is the force applied to an object,
- m is the mass of the object,
- a is the acceleration of the object.
Work-Energy Theorem
W = ΔKE
Where:
- W is the work done on an object,
- ΔKE is the change in kinetic energy.
Kinetic Energy
KE = 1/2mv2
Where:
- KE is the kinetic energy,
- m is the mass of the object,
- v is the velocity of the object.
Potential Energy (Gravitational)
PE = mgh
Where:
- PE is the potential energy,
- m is the mass,
- g is the acceleration due to gravity,
- h is the height.
Hooke's Law (Spring Force)
Fs = −kx
Where:
- Fs is the spring force,
- k is the spring constant,
- x is the displacement from the equilibrium position.
Newton's Law of Universal Gravitation
F = G ⋅ m1 ⋅ m2 / r2
Where:
- F is the gravitational force between two masses,
- G is the gravitational constant,
- m1 and m2 are the masses,
- r is the distance between the centers of the masses.
Below are some important kinematics formulas:
Displacement (s)
s = ut + 1/2 at2
Where:
- s is the displacement.
- u is the initial velocity
- a is the acceleration,
- t is the time.
Final Velocity(v)
v = u+ at
Where:
- v is the final velocity,
- u is the initial velocity,
- a is the acceleration,
- t is the time.
Kinematic Third Equation of Motion
v2 = u2 + 2as
Where:
- v is the final velocity,
- u is the initial velocity,
- a is the acceleration,
- s is the displacement.
Average Velocity (v)
v = Δx / Δt
Where:
- v is the average velocity.
- Δx is the displacement.
- Δt is the time interval.
Acceleration (a)
a = Δv /Δt
Where:
a is the acceleration.
Δv is the change in velocity.
Δt is the time interval.
Few important electricity formulas are given below:
Electric Current (I)
I = Q/t
Where:
- I is the electric current (measured in Amperes, A).
- Q is the charge that passes through a given point.
- t is the time taken.
Electric Charge (Q)
Q = I × t
Where:
- Q is the electric charge (measured in Coulombs, C).
- I is the electric current.
- t is the time taken.
Ohm's Law
V = IR
Where:
- V is the voltage,
- I is the current,
- R is the resistance.
Power
P = VI
Where:
- P is the power,
- I is the current,
- V is the voltage.
Resistance
R = ρl / A
Where:
- R is the resistance,
- ρ is resistivity,
- l is length, and
- A is area
Watt's Law
P = I²R or P = V²/R
Where:
- R is the resistance,
- I is Current, and
- V is Voltage
Electric Energy
P = W x T
where:
- P is power,
- W is energy, and
- T is time
Voltage
V = E / Q
where
- E is energy, and
- Q is charge
Important Electromagnetism Formulas are given below:
Electric Field (E)
E = F/q
Where:
- E is the electric field.
- F is the force experienced by the charge.
- q is the magnitude of the charge.
Faraday's Law of Electromagnetic Induction
ε = dΦ/dt
Where:
- ε is the induced EMF.
- Φ is the magnetic flux through the loop.
- t is time.
Magnetic Force on a Moving Charge
F = qvBsinθ
Where:
- F is the magnetic force,
- q is the charge,
- v is the velocity,
- B is the magnetic field strength,
- θ is the angle between v and B.
Gauss' Law for Electric Field
Φ = q/εo
Where:
- εo is the electric permittivity of free space
- Φ is the magnetic flux through the loop.
- q is the net charge enclosed by the surface.
Electric Potential (Voltage)
V = W/q
Where:
- V is the electric potential (voltage).
- W is the electric potential energy.
- q is the charge.
Few important optics formula are:
Snell's Law (Refraction)
n1 sinθ1 = n2 sinθ2
Where:
- n1 incident index
- n2 refracted index
- θ1 incident angle
- θ2 refracted angle
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens,
- u is the object distance,
- v is the image distance.
Magnification for Lenses
m = −v/u
Where:
- m is the magnification,
- v is the image distance,
- u is the object distance.
Magnifying Power
M = 1 + d/f
Where:
- M is the magnifying power
- f is the focal distance
- d is the distance between the object and the lens
1/f = 1/i + 1/o
Where:
- f is the focal length.
- i is the image distance.
- o is the object distance.
Important sound formulas are given below:
Speed of Sound
v = √(B/p)
Where:
- v is the speed of sound,
- B is the bulk modulus of the medium,
- ρ is the density of the medium.
Wavelength (λ)
λ = v/f
Where:
- λ is Wavelength
- v is Speed of sound
- f is Frequency of the sound wave
Frequency (f)
f = v / λ
Where:
f is Frequency
v is Speed of sound
λ is Wavelength
Acoustic Impedance (Z)
Z = ρ × c
Where:
- Z is Acoustic impedance
- ρ is Density of the medium
- c is Speed of sound in the medium
Few important formulas related to fluid mechanics are:
Density
ρ = mV
Where:
- ρ is density of fluid
- m is mass, and
- v is volume
Pressure
P = F/A
Where:
- P is the pressure of the fluid,
- F is applied Force,
- A is area
Pressure at a Depth h in a Fluid of Constant Density
p = po + ρgh
where:
- p is pressure at height h
- po is the pressure at the fluid's surface,
- ρ is the density of the fluid,
- g is the acceleration due to gravity, and
- h is the depth to which the object is submerged
Viscosity
η = FL/vA
Where:
- η is fluid viscosity
- F is force
- L is distance between the plates
- V is constant velocity
- A is area of the plate
Pascal's Law
F = PA
Where:
- F is applied Force
- P is Pressure, and
- A is area under cross-section.
Reynolds Number (Re)
Re = pvL/μ
Where:
- ρ is the density of the fluid.
- v is the velocity of the fluid.
- L is a characteristic length (e.g., diameter of the pipe).
- μ is the dynamic viscosity of the fluid.
Important thermodynamics formulas are illustrated below:
First Law of Thermodynamics (Energy Conservation)
ΔU = Q − W
Where:
- ΔU is the change in internal energy,
- Q is the heat added to the system,
- W is the work done by the system.
Work Done in Isothermal Process (Ideal Gas)
W = nRTln(Vf/Vi)
Where:
- W is the work done,
- n is the number of moles of gas,
- R is the ideal gas constant,
- T is the temperature,
- Vf is the final volume,
- Vi is the initial volume.
Heat Transfer (Constant Pressure)
Q = nCp ΔT
Where:
- Q is the heat added or removed,
- n is the number of moles of gas,
- Cp is the specific heat at constant pressure,
- ΔT is the change in temperature.
Ideal Gas Law
PV = nRT
Where:
- P is the pressure of the gas.
- V is the volume of the gas.
- n is the number of moles of gas.
- R is the gas constant.
- T is the temperature of the gas.
Entropy Change
ΔS = Q/T
Where:
- ΔS is the change in entropy.
- Q is the heat.
- T is the temperature.
Gibbs Free Energy
ΔG = ΔH − TΔS
Where:
- ΔG is the change in Gibbs free energy,
- ΔH is the change in enthalpy,
- ΔS is the change in entropy, and
- T is the absolute temperature
Important formulas related to wave are described below:
Wave Velocity (v)
v = f × λ
Where:
- v = Wave velocity (in meters per second, m/s)
- f = Frequency of the wave (in Hertz, Hz)
- λ = Wavelength of the wave (in meters, m)
Frequency (f)
f = 1/T
Where:
- f = Frequency (in Hertz, Hz)
- T = Time period of one wave cycle (in seconds, s)
Wavelength (λ)
λ = v/f
Where:
- λ = Wavelength (in meters, m)
- v = Wave velocity (in meters per second, m/s)
- f = Frequency (in Hertz, Hz)
Period (T)
T = 1/f
Where:
- T = Period (in seconds, s)
- f = Frequency (in Hertz, Hz)
Intensity (I)
I = P/A
where:
- P is the power
- A is the area.
Example 1: A stretched string has a displacement of 20 cm and a spring constant of 50Nm−1. Calculate the potential energy that the stretched string contains.
Solution:
The parameters that are given are
k = 50Nm−1
x is equal to 20 cm, or 0.2 m.
Potential energy is what it will be.
P.E. = 1/2 k × x2
P.E =3/4 X 50 × (0.2)2
P.E = 1 J
Example 2: When x is in meters and t is in seconds, a body travels down the x-axis in accordance with the equation x = 1 – 2 t + 3t2. Determine the body's acceleration at t = 3s.
Solution:
As we have
x = 1 - 2 t + 3t2 then;
Speed v = dx/dt = d(1 - 2t + 3t2)/dt = −2 + 6t
Now Acceleration a = dv/dt = d(−2+6t)/dt = 6
acceleration when t is 3s = 6 m/s2
Example 3: Determine the weight of an item that weighs 50 kg on Earth.
Solution:
We know, weight = m × g
w = (50 × 9.8) kg m/s2
w = 490 N
Example 4: A person travels in 10 seconds from Point A to Point B and returns in 8 seconds. Determine the person's average speed if the distance is 36 meters between A and B.
Solution:
This distance traveled in total is 36 + 36 = 72 meters.
18 seconds was the total time taken.
Thus, average speed is equal to the total distance traveled divided by total time.
average speed = 72/18 = 4 m/s.
Hence the average speed of the person is 4 m/s.
Example 5: Determine the mass of an object having a kinetic energy of 100J and a velocity of 5 m/s.
Solution:
We know, KE = ½ mv2.
100 = ½ x m x 5 x 5.
100 = 25 m/2
m = (100 × 2)/25
m = 8 kg
Practice Problems
Problems 1: Determine the displacement that an object traveling at a speed of 60 m/s will cover in 3 seconds.
Problems 2: A 50 cm long, thin rod has an evenly distributed total charge of 5 mC over it. Determine the linear density of charges.
Problems 3: A automobile with a mass of 250 kg is moving at a speed of 10 meters per second. What is the kinetic energy of it?
Problems 4: 400kcal of heat is required for the phase transition of a 2 kilogram material. Calculate the heat it contains latently.
Problems 5: A cube immersed in water with a side length of 0.1 meters and a density of 800 kg/m3. Determine if the cube will sink or float by computing the buoyant force acting on it.
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