CBSE · Class 11 · Physics

Physics Formula Sheet

110 formulas across 14 chapters — with variables explained and exam tips where needed.

2. Units and Measurements 3. Motion in a Straight Line 4. Motion in a Plane 5. Laws of Motion 6. Work, Energy and Power 7. System of Particles and Rotational Motion 8. Gravitation 9. Mechanical Properties of Solids 10. Mechanical Properties of Fluids 11. Thermal Properties of Matter 12. Thermodynamics 13. Kinetic Theory of Gases 14. Oscillations 15. Waves

Ch 2Units and Measurements(8 formulas)

Dimensional formula of velocity

[v] = [M⁰LT⁻¹]

Dimensional formula of force

[F] = [MLT⁻²]

Dimensional formula of energy

[E] = [ML²T⁻²]

Dimensional formula of pressure

[P] = [ML⁻¹T⁻²]

Significant figures: addition/subtraction

Result has fewest decimal places of any operand

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For multiplication/division, result has fewest significant figures

Absolute error

Δa = |a_mean − aᵢ|

Relative error

Relative error = Δa / a_mean

Percentage error

% error = (Δa / a_mean) × 100

Ch 3Motion in a Straight Line(7 formulas)

First equation of motion

v = u + at

u = initial velocity, v = final velocity, a = acceleration, t = time

Second equation of motion

s = ut + ½at²

s = displacement

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Use this when time is given and displacement is asked

Third equation of motion

v² = u² + 2as

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Use this when time is not given

Average velocity

v_avg = (u + v)/2 (only for uniform acceleration)

Displacement in nth second

sₙ = u + a(2n − 1)/2

Relative velocity

v_AB = v_A − v_B

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If moving in same direction: subtract; opposite direction: add

Free fall acceleration

a = g = 9.8 m/s² (downward)

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Take downward as positive; then u = 0 for a body dropped from rest

Ch 4Motion in a Plane(8 formulas)

Projectile: Range

R = u²sin2θ / g

u = initial speed, θ = angle of projection, g = 9.8 m/s²

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Maximum range occurs at θ = 45°

Projectile: Maximum height

H_max = u²sin²θ / 2g

Projectile: Time of flight

T = 2u sinθ / g

Projectile: Horizontal velocity

v_x = u cosθ (constant throughout)

Projectile: Vertical velocity

v_y = u sinθ − gt

Centripetal acceleration

aₓ = v²/r = ω²r

v = speed, r = radius, ω = angular velocity

Centripetal force

F = mv²/r = mω²r

Relation: linear and angular velocity

v = ωr

Ch 5Laws of Motion(7 formulas)

Newton's Second Law

F = ma

F = net force (N), m = mass (kg), a = acceleration (m/s²)

Impulse

N·s or kg·m/s

J = FΔt = Δp = m(v − u)

Static friction (max)

f_s = μₛN

μₛ = coefficient of static friction, N = normal force

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Static friction ≤ μₛN; it equals applied force until this limit

Kinetic friction

f_k = μₖN

μₖ = coefficient of kinetic friction

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μₖ < μₛ always — kinetic friction is less than maximum static friction

Pseudo force (non-inertial frame)

F_pseudo = −ma_frame

a_frame = acceleration of non-inertial frame

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Directed opposite to the frame's acceleration

Normal force on inclined plane

N = mg cosθ

Acceleration on frictionless incline

a = g sinθ

Ch 6Work, Energy and Power(8 formulas)

Work done by constant force

W = Fs cosθ

F = force, s = displacement, θ = angle between F and s

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W = 0 if F ⊥ s (e.g. centripetal force does no work)

Kinetic energy

KE = ½mv²

Gravitational potential energy

PE = mgh

Work-energy theorem

W_net = ΔKE = KE_final − KE_initial

Conservation of mechanical energy

KE + PE = constant (no friction)

Power

W (Watt)

P = W/t = Fv cosθ

Spring potential energy

PE = ½kx²

k = spring constant, x = compression/extension

Elastic collision: kinetic energy

KE conserved | v₁' = (m₁−m₂)u₁/(m₁+m₂) | v₂' = 2m₁u₁/(m₁+m₂)

Ch 7System of Particles and Rotational Motion(11 formulas)

Torque

N·m

τ = r × F = rF sinθ

Angular momentum

kg·m²/s

L = Iω = mvr sinθ

Newton's second law (rotation)

τ = Iα

I = moment of inertia, α = angular acceleration

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Rotational analogue of F = ma

Moment of inertia: thin rod (centre)

I = ML²/12

Moment of inertia: thin rod (end)

I = ML²/3

Moment of inertia: disc (centre)

I = MR²/2

Moment of inertia: ring (centre)

I = MR²

Moment of inertia: solid sphere

I = 2MR²/5

Parallel axis theorem

I = I_cm + Md²

d = distance from CM to new axis

Rolling body KE

KE_total = ½mv² + ½Iω² = ½mv²(1 + I/mR²)

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For a sphere: KE = 7/10 mv²; for a cylinder: KE = 3/4 mv²

Conservation of angular momentum

L = Iω = constant (when τ_net = 0)

Ch 8Gravitation(8 formulas)

Newton's law of gravitation

F = Gm₁m₂/r²

G = 6.674×10⁻¹¹ N·m²/kg²

Acceleration due to gravity at surface

g = GM/R²

M = mass of Earth, R = radius of Earth

Variation of g with height h

g_h = g(1 − 2h/R) for h << R

Variation of g with depth d

g_d = g(1 − d/R)

Orbital velocity

v₀ = √(GM/r)

r = orbital radius

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At surface r = R, so v₀ = √(gR)

Escape velocity

v_e = √(2GM/R) = √(2gR)

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Escape velocity = √2 × orbital velocity at surface

Kepler's third law

T² ∝ r³ or T² = (4π²/GM) r³

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More massive central body → faster orbital period

Gravitational potential energy

U = −GMm/r

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Negative value: bound system; approaches 0 as r → ∞

Ch 9Mechanical Properties of Solids(7 formulas)

Stress

N/m² or Pa

Stress = F/A

F = applied force, A = cross-sectional area

Strain

Strain = ΔL/L (longitudinal) or Δx/L (shear)

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Strain is dimensionless

Young's modulus

Y = (F/A) / (ΔL/L) = Stress / Longitudinal strain

Bulk modulus

B = −ΔP / (ΔV/V)

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Negative sign: pressure increase → volume decrease

Modulus of rigidity

η = Shear stress / Shear strain

Hooke's Law

Stress ∝ Strain (within elastic limit)

Elastic potential energy per unit volume

u = ½ × stress × strain = ½ Y (strain)²

Ch 10Mechanical Properties of Fluids(8 formulas)

Pressure at depth h

P = P₀ + ρgh

P₀ = atmospheric pressure, ρ = fluid density

Pascal's law

Pressure applied to enclosed fluid is transmitted equally in all directions

Bernoulli's equation

P + ½ρv² + ρgh = constant

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Energy conservation for ideal fluid flow — fast flow → low pressure

Continuity equation

A₁v₁ = A₂v₂

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Narrower pipe → faster flow

Stokes' law (viscous drag)

F = 6πηrv

η = coefficient of viscosity, r = radius of sphere, v = velocity

Terminal velocity

v_t = 2r²(ρ − σ)g / 9η

σ = density of fluid

Surface tension

N/m

T = F/L

Excess pressure inside bubble (soap)

ΔP = 4T/r

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Soap bubble has two surfaces; liquid drop has one surface so ΔP = 2T/r

Ch 11Thermal Properties of Matter(7 formulas)

Linear thermal expansion

ΔL = αLΔT

α = coefficient of linear expansion, L = original length, ΔT = temperature change

Volumetric thermal expansion

ΔV = γVΔT

γ = 3α for isotropic solids

Heat absorbed / released

Q = mcΔT

m = mass, c = specific heat capacity, ΔT = temperature change

Latent heat

Q = mL

L = specific latent heat

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Temperature stays constant during phase change

Stefan-Boltzmann law

P = εσAT⁴

σ = 5.67×10⁻⁸ W/m²·K⁴, ε = emissivity, A = area, T = temperature in K

Wien's displacement law

λ_max T = 2.898×10⁻³ m·K

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Hotter body emits at shorter (bluer) wavelengths

Newton's law of cooling

dT/dt = −k(T − T₀)

T₀ = ambient temperature, k = cooling constant

Ch 12Thermodynamics(7 formulas)

First law of thermodynamics

ΔU = Q − W

ΔU = change in internal energy, Q = heat added to system, W = work done by system

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Sign convention: Q +ve when added to system; W +ve when done BY system

Work done by gas (isobaric)

W = PΔV = P(V₂ − V₁)

Efficiency of Carnot engine

η = 1 − T₂/T₁

T₁ = source temperature (K), T₂ = sink temperature (K)

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Always use temperatures in Kelvin

COP of refrigerator

COP = T₂ / (T₁ − T₂) = Q₂/W

Q₂ = heat extracted from cold reservoir

Entropy change

J/K

ΔS = Q/T (reversible process)

Relation for Cp and Cv

Cp − Cv = R

R = 8.314 J/mol·K

Adiabatic process

PVᵞ = constant | TV^(γ−1) = constant

γ = Cp/Cv

Ch 13Kinetic Theory of Gases(8 formulas)

Ideal gas law

PV = nRT

n = moles, R = 8.314 J/mol·K, T = temperature in K

Kinetic energy per molecule

KE = 3/2 kT

k = 1.38×10⁻²³ J/K (Boltzmann constant)

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Average KE depends only on temperature, not mass

RMS speed

v_rms = √(3RT/M) = √(3kT/m)

M = molar mass, m = mass of one molecule

Average speed

v_avg = √(8RT/πM)

Most probable speed

v_mp = √(2RT/M)

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Speeds order: v_mp < v_avg < v_rms

Degrees of freedom: monatomic gas

f = 3 | U = 3/2 nRT

Degrees of freedom: diatomic gas

f = 5 | U = 5/2 nRT

Mean free path

λ = 1/(√2 πd²n)

d = diameter of molecule, n = number density

Ch 14Oscillations(8 formulas)

Displacement in SHM

x = A sin(ωt + φ)

A = amplitude, ω = angular frequency, φ = initial phase

Angular frequency of spring-mass

ω = √(k/m) → T = 2π√(m/k)

k = spring constant, m = mass

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T depends on mass and spring constant, not amplitude

Time period of simple pendulum

T = 2π√(l/g)

l = effective length

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T independent of mass and amplitude (for small oscillations)

Velocity in SHM

v = ω√(A² − x²)

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Maximum velocity v_max = ωA at x = 0

Acceleration in SHM

a = −ω²x

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Acceleration is always directed towards mean position

Total energy in SHM

E = ½kA² = ½mω²A²

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Total energy is constant; independent of position

Kinetic energy in SHM

KE = ½mω²(A² − x²)

Potential energy in SHM

PE = ½mω²x²

Ch 15Waves(8 formulas)

Wave speed

m/s

v = fλ

f = frequency (Hz), λ = wavelength (m)

Wave speed on string

v = √(T/μ)

T = tension, μ = linear mass density (kg/m)

Wave speed in gas

v = √(γP/ρ)

γ = ratio of specific heats, P = pressure, ρ = density

Speed of sound in air

v ≈ 331 + 0.6T m/s

T = temperature in °C

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Speed increases with temperature

Standing waves: nodes and antinodes

λ = 2L/n for both ends fixed | λ = 4L/(2n−1) for one end open

Fundamental frequency (string)

f₁ = v/2L = (1/2L)√(T/μ)

Doppler effect (source moving towards observer)

f' = f(v + v₀) / (v − v_s)

v₀ = observer speed, v_s = source speed

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Use +v₀ if observer moves towards source, −v₀ if away

Beats

Beat frequency = |f₁ − f₂|

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Beats are heard when two close frequencies are superimposed

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