Complete Class 11 Physics Formulas

Comprehensive reference with examples, calculators, and board-specific content for CBSE, ICSE & State Boards

Physics Topics

Physical World & Measurement
Kinematics
Laws of Motion
Work, Energy & Power
Motion of System of Particles
Gravitation
Mechanical Properties
Thermal Properties
Thermodynamics
Kinetic Theory of Gases
Oscillations
Waves

Physical World & Measurement

Density

All Boards

ρ = m/V

Density is defined as mass per unit volume. It’s a scalar quantity with SI unit kg/m³. Density indicates how much mass is contained in a given volume.

Variables:

ρ Density (kg/m³)
m Mass (kg)
V Volume (m³)

Example

If a block of wood has mass 500 g and volume 625 cm³, its density is:

ρ = 500 g / 625 cm³ = 0.8 g/cm³ = 800 kg/m³

Calculate Density

Mass (kg)

Volume (m³)

Relative Error

CBSE & State

Relative Error = Δa / a

Relative error is the ratio of absolute error to the actual value of the quantity being measured. It gives the proportion of error relative to the measurement.

Variables:

Δa Absolute Error
a Measured Value

Example

If the measured length of a rod is 25.2 cm with an absolute error of 0.1 cm, then:

Relative Error = 0.1 / 25.2 ≈ 0.004 (or 0.4%)

Significant Figures Rules

All Boards

Rules for Mathematical Operations

Significant figures indicate the precision of a measurement. Rules vary for different mathematical operations.

Rules:

Addition/Subtraction:

Result has same decimal places as the number with fewest decimal places

Multiplication/Division:

Result has same significant figures as the number with fewest significant figures

Example

12.5 + 3.24 = 15.7 (1 decimal place)

2.5 × 3.42 = 8.6 (2 significant figures)

Kinematics

Equations of Motion

All Boards

v = u + at
s = ut + ½at²
v² = u² + 2as

These equations describe the motion of an object with constant acceleration. They relate initial velocity, final velocity, acceleration, time, and displacement.

Variables:

u Initial Velocity (m/s)
v Final Velocity (m/s)
a Acceleration (m/s²)
t Time (s)
s Displacement (m)

Example

A car starts from rest and accelerates at 2 m/s² for 5 seconds. Find its final velocity and displacement.

v = 0 + (2)(5) = 10 m/s

s = 0 + ½(2)(5)² = 25 m

Calculate Motion

Initial Velocity (m/s)

Acceleration (m/s²)

Time (s)

Projectile Motion

CBSE & ICSE

Time of flight: T = 2u sinθ / g
Maximum height: H = u² sin²θ / 2g
Horizontal range: R = u² sin2θ / g

These equations describe the motion of a projectile launched with initial velocity u at an angle θ to the horizontal, under constant gravitational acceleration g.

Variables:

u Initial Velocity (m/s)
θ Launch Angle (degrees)
g Gravity (m/s²)
T Time of Flight (s)
H Max Height (m)
R Horizontal Range (m)

Example

A ball is thrown with velocity 20 m/s at 30° to the horizontal. Find its time of flight and range (g = 10 m/s²).

T = 2×20×sin30° / 10 = 2 seconds

R = (20)²×sin60° / 10 = 34.64 m

Relative Velocity

All Boards

v_AB = v_A – v_B

The velocity of object A relative to object B is the vector difference of their velocities with respect to a common reference frame.

Variables:

v_AB Velocity of A relative to B
v_A Velocity of A
v_B Velocity of B

Example

If car A moves east at 60 km/h and car B moves east at 40 km/h, then:

v_AB = 60 – 40 = 20 km/h east

Laws of Motion

Newton’s Second Law

All Boards

F = ma

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is the foundation of classical mechanics.

Variables:

F Force (N)
m Mass (kg)
a Acceleration (m/s²)

Example

What force is needed to accelerate a 5 kg object at 3 m/s²?

F = 5 × 3 = 15 N

Calculate Force

Mass (kg)

Acceleration (m/s²)

Friction

CBSE & State

f = μN

The force of friction is equal to the coefficient of friction (μ) multiplied by the normal force (N). Friction opposes relative motion between surfaces in contact.

Variables:

f Frictional Force (N)
μ Coefficient of Friction
N Normal Force (N)

Example

A 10 kg box rests on a horizontal surface with μ = 0.4. What is the frictional force?

N = mg = 10 × 9.8 = 98 N

f = 0.4 × 98 = 39.2 N

Circular Motion

All Boards

F = mv²/r

For an object moving in a circular path, the centripetal force is directed toward the center and is equal to the mass times the square of velocity divided by radius.

Variables:

F Centripetal Force (N)
m Mass (kg)
v Velocity (m/s)
r Radius (m)

Example

A 2 kg object moves in a circle of radius 5 m at 4 m/s. Centripetal force is:

F = (2 × 4²) / 5 = 32 / 5 = 6.4 N

Work, Energy & Power

Work Done

All Boards

W = F × s × cosθ

Work is done when a force causes displacement. It’s the product of force, displacement, and the cosine of the angle between them.

Variables:

W Work (J)
F Force (N)
s Displacement (m)
θ Angle between F and s

Example

A force of 10 N moves an object 5 m in the direction of the force. Work done is:

W = 10 × 5 × cos0° = 50 J

Kinetic Energy

All Boards

K.E. = ½mv²

Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and the square of the velocity of the object.

Variables:

K.E. Kinetic Energy (J)
m Mass (kg)
v Velocity (m/s)

Example

A 2 kg object moving at 3 m/s has kinetic energy:

K.E. = ½ × 2 × (3)² = 9 J

Potential Energy

All Boards

P.E. = mgh

Potential energy is the energy stored in an object due to its position in a gravitational field. It depends on mass, gravitational acceleration, and height.

Variables:

P.E. Potential Energy (J)
m Mass (kg)
g Gravity (m/s²)
h Height (m)

Example

A 5 kg object at height 10 m has potential energy:

P.E. = 5 × 9.8 × 10 = 490 J

Power

All Boards

P = W/t

Power is the rate at which work is done or energy is transferred. It measures how quickly work is completed.

Variables:

P Power (W)
W Work (J)
t Time (s)

Example

If 500 J of work is done in 10 seconds, the power is:

P = 500 / 10 = 50 W

Motion of System of Particles

Center of Mass

All Boards

x_cm = (m₁x₁ + m₂x₂ + …) / (m₁ + m₂ + …)

The center of mass is the point where the entire mass of a system can be considered to be concentrated for translational motion.

Variables:

x_cm Center of Mass Position
m₁, m₂ Masses of particles
x₁, x₂ Positions of particles

Example

Two masses 2 kg and 3 kg are at positions x=1 m and x=4 m. Center of mass is:

x_cm = (2×1 + 3×4) / (2+3) = 14/5 = 2.8 m

Linear Momentum

All Boards

p = mv

Linear momentum is the product of an object’s mass and velocity. It’s a vector quantity that represents the quantity of motion.

Variables:

p Momentum (kg·m/s)
m Mass (kg)
v Velocity (m/s)

Example

A 0.5 kg ball moving at 20 m/s has momentum:

p = 0.5 × 20 = 10 kg·m/s

Gravitation

Newton’s Law of Gravitation

All Boards

F = G(m₁m₂)/r²

Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Variables:

F Gravitational Force (N)
G Gravitational Constant (6.674×10⁻¹¹ N·m²/kg²)
m₁, m₂ Masses (kg)
r Distance between centers (m)

Example

Two 100 kg spheres are 2 m apart. Gravitational force is:

F = (6.67×10⁻¹¹ × 100 × 100) / (2)² = 1.67×10⁻⁷ N

Gravitational Potential Energy

All Boards

U = -G(m₁m₂)/r

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It is negative because gravity is an attractive force.

Variables:

U Potential Energy (J)
G Gravitational Constant
m₁, m₂ Masses (kg)
r Distance between centers (m)

Example

Potential energy between Earth and a 1 kg mass at Earth’s surface:

U = -(6.67×10⁻¹¹ × 5.97×10²⁴ × 1) / (6.37×10⁶) = -6.25×10⁷ J

Mechanical Properties of Solids & Fluids

Stress

All Boards

σ = F/A

Stress is the internal resisting force per unit area developed in a material when an external force is applied.

Variables:

σ Stress (Pa or N/m²)
F Force (N)
A Area (m²)

Example

A force of 1000 N is applied to a 0.01 m² area. Stress is:

σ = 1000 / 0.01 = 100,000 Pa = 100 kPa

Strain

All Boards

ε = ΔL/L

Strain is the ratio of change in dimension to the original dimension of a material when subjected to stress.

Variables:

ε Strain (dimensionless)
ΔL Change in Length (m)
L Original Length (m)

Example

A 2 m long wire stretches by 0.002 m. Strain is:

ε = 0.002 / 2 = 0.001

Thermal Properties of Matter

Heat Transfer

All Boards

Q = mcΔT

The amount of heat transferred to or from a substance is equal to the product of its mass, specific heat capacity, and temperature change.

Variables:

Q Heat (J)
m Mass (kg)
c Specific Heat (J/kg·K)
ΔT Temperature Change (K)

Example

Heating 2 kg of water (c=4186 J/kg·K) from 20°C to 80°C requires:

Q = 2 × 4186 × 60 = 502,320 J

Linear Expansion

All Boards

ΔL = αLΔT

The change in length of a material due to temperature change is proportional to the original length and the temperature change.

Variables:

ΔL Change in Length (m)
α Coefficient of Linear Expansion (K⁻¹)
L Original Length (m)
ΔT Temperature Change (K)

Example

A 10 m steel rail (α=12×10⁻⁶ K⁻¹) heated from 20°C to 40°C expands by:

ΔL = (12×10⁻⁶) × 10 × 20 = 0.0024 m = 2.4 mm

Thermodynamics

First Law of Thermodynamics

All Boards

ΔU = Q – W

The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Variables:

ΔU Change in Internal Energy (J)
Q Heat Added (J)
W Work Done by System (J)

Example

A system absorbs 500 J of heat and does 200 J of work. Internal energy change is:

ΔU = 500 – 200 = 300 J

Ideal Gas Law

All Boards

PV = nRT

The pressure and volume of a gas are directly proportional to the amount of gas and its absolute temperature.

Variables:

P Pressure (Pa)
V Volume (m³)
n Number of Moles
R Gas Constant (8.314 J/mol·K)
T Temperature (K)

Example

2 moles of gas at 300 K in 0.05 m³ container has pressure:

P = (2 × 8.314 × 300) / 0.05 = 99,768 Pa

Kinetic Theory of Gases

Pressure of Ideal Gas

All Boards

P = (1/3)ρv²

The pressure exerted by an ideal gas is proportional to the density of the gas and the square of the root mean square speed of its molecules.

Variables:

P Pressure (Pa)
ρ Density (kg/m³)
v RMS Speed (m/s)

Example

A gas with density 1.2 kg/m³ and RMS speed 500 m/s exerts pressure:

P = (1/3) × 1.2 × (500)² = 100,000 Pa

Average Kinetic Energy

All Boards

K.E. = (3/2)kT

The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.

Variables:

K.E. Kinetic Energy (J)
k Boltzmann Constant (1.38×10⁻²³ J/K)
T Temperature (K)

Example

At room temperature (300 K), average molecular kinetic energy is:

K.E. = (3/2) × (1.38×10⁻²³) × 300 = 6.21×10⁻²¹ J

Oscillations

Simple Harmonic Motion

All Boards

x = A sin(ωt + φ)

The displacement in simple harmonic motion varies sinusoidally with time, with amplitude A, angular frequency ω, and phase constant φ.

Variables:

x Displacement (m)
A Amplitude (m)
ω Angular Frequency (rad/s)
t Time (s)
φ Phase Constant (rad)

Example

A particle in SHM with A=0.1 m, ω=2π rad/s at t=0, x=0. Displacement at t=0.25 s is:

x = 0.1 × sin(2π×0.25) = 0.1 × sin(π/2) = 0.1 m

Period of Simple Pendulum

All Boards

T = 2π√(L/g)

The period of a simple pendulum depends only on its length and the acceleration due to gravity, not on the mass or amplitude.

Variables:

T Period (s)
L Length (m)
g Gravity (m/s²)

Example

A 1 m long pendulum has period:

T = 2π√(1/9.8) ≈ 2π√0.102 ≈ 2.01 s

Waves

Wave Equation

All Boards

v = fλ

The speed of a wave is equal to the product of its frequency and wavelength. This fundamental relationship applies to all types of waves.

Variables:

v Wave Speed (m/s)
f Frequency (Hz)
λ Wavelength (m)

Example

A sound wave with frequency 440 Hz and wavelength 0.75 m has speed:

v = 440 × 0.75 = 330 m/s

Doppler Effect

All Boards

f’ = f(v ± v₀)/(v ∓ vₛ)

The apparent change in frequency of a wave due to relative motion between the source and observer.

Variables:

f’ Apparent Frequency (Hz)
f Actual Frequency (Hz)
v Wave Speed (m/s)
v₀ Observer Speed (m/s)
vₛ Source Speed (m/s)

Example

A car horn (f=500 Hz) approaches at 30 m/s. For stationary observer (v=340 m/s):

f’ = 500 × 340 / (340 – 30) ≈ 548 Hz

Physics Topics

Physical World & Measurement

Variables:

Example

Calculate Density

Variables:

Example

Rules:

Example

Kinematics

Variables:

Example

Calculate Motion

Variables:

Example

Variables:

Example

Laws of Motion

Variables:

Example

Calculate Force

Variables:

Example

Variables:

Example

Work, Energy & Power

Variables:

Example

Variables:

Example

Variables:

Example

Variables:

Example

Motion of System of Particles

Variables:

Example

Variables:

Example

Gravitation

Variables:

Example

Variables:

Example

Mechanical Properties of Solids & Fluids

Variables:

Example

Variables:

Example

Thermal Properties of Matter

Variables:

Example

Variables:

Example

Thermodynamics

Variables:

Example

Variables:

Example

Kinetic Theory of Gases

Variables:

Example

Variables:

Example

Oscillations

Variables:

Example

Variables:

Example

Waves

Variables:

Example

Variables:

Example

Related Posts

Leave a Comment Cancel Reply