Class 11 Physics Formula Sheet (PDF) — All Important Formulas Free
Free class 11 physics formula sheet — all 69 key formulas on one page, downloadable as PDF for fast revision before CBSE board exams. No signup.
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Complete formula sheet for CBSE Class 11 Physics. Covers mechanics, thermodynamics, waves, and properties of matter. SI units throughout.
Units & Measurement
| Formula | Expression |
|---|---|
| Dimensional Analysis | [M^a L^b T^c I^d K^e] — M = mass, L = length, T = time, I = current, K = temperature, N = amount of substance |
| Standard Units | Length (m), Mass (kg), Time (s), Current (A), Temperature (K) — SI base units. Derived units combine these: velocity (m/s), force (N=kg⋅m/s²) |
| Uncertainty & Errors | Δx/x = ±(Δa/a + Δb/b) for products/quotients — Percentage error = (Δx/x)×100%. Random errors reduce with multiple measurements. |
Kinematics
| Formula | Expression |
|---|---|
| Position & Displacement | s = x₂ - x₁ (vector), distance = |s| (scalar) — Displacement can be negative (change in position) |
| Velocity & Acceleration | v = ds/dt, a = dv/dt = d²s/dt² — Average: v_avg = Δs/Δt, a_avg = Δv/Δt |
| Equation of Motion 1 | v = u + at — Linear motion, constant acceleration |
| Equation of Motion 2 | s = ut + ½at² — Displacement formula |
| Equation of Motion 3 | v² = u² + 2as — Connects velocity, acceleration, displacement |
| Projectile Motion | x = v₀ₓt, y = v₀ᵧt - ½gt², tan θ = v₀ᵧ/v₀ₓ — x-axis: uniform, y-axis: uniformly accelerated (g = 10 m/s²) |
| Range & Max Height | R = v₀² sin 2θ / g, H = v₀² sin² θ / (2g) — R maximum at θ = 45°. H for vertical component only. |
Laws of Motion
| Formula | Expression |
|---|---|
| Newton's First Law | F_net = 0 → a = 0 (equilibrium) — Object at rest/uniform motion stays so unless net force acts |
| Newton's Second Law | F_net = ma → a = F_net/m — F in newtons (N), m in kg, a in m/s² |
| Newton's Third Law | F_AB = -F_BA — Action-reaction forces are equal, opposite, on different objects |
| Friction | f_s ≤ μ_s N, f_k = μ_k N — μ_s = static friction coefficient, μ_k = kinetic, N = normal force |
| Weight & Normal Force | W = mg, N = mg cos θ (on incline) — Weight always downward, normal force perpendicular to surface |
| Tension in String | T = ma + mg (for acceleration upward) — Free body diagram essential. For pulley systems, use F_net on each mass. |
Work, Energy & Power
| Formula | Expression |
|---|---|
| Work Done | W = F⃗ · s⃗ = Fs cos θ — W in joules (J). Positive: force in direction of motion, Negative: against motion |
| Kinetic Energy | Ek = ½mv² — Energy due to motion. KE always ≥ 0 |
| Potential Energy (Gravity) | Ep = mgh — Relative to reference level. Change in PE = mg(h₂ - h₁) |
| Work-Energy Theorem | W_net = ΔEk = ½m(v₂² - v₁²) — Net work equals change in kinetic energy |
| Conservation of Energy | E_total = Ek + Ep = constant (no friction) — Mechanical energy conserved in isolated systems |
| Power | P = W/t = Fv cos θ — P in watts (W). Average vs instantaneous power |
| Elastic Potential Energy | Ep = ½kx² — k = spring constant (N/m), x = extension (m) |
Rotational Motion
| Formula | Expression |
|---|---|
| Angular Displacement | θ = s/r (in radians) — s = arc length, r = radius. 1 radian = 57.3°, 2π rad = 360° |
| Angular Velocity | ω = dθ/dt, v = rω — ω in rad/s. Linear velocity v at circumference |
| Angular Acceleration | α = dω/dt, a_t = rα — α in rad/s². a_t = tangential acceleration |
| Centripetal Acceleration | a_c = v²/r = ω²r — Directed toward center. Always perpendicular to velocity |
| Moment of Inertia | I = Σmᵢrᵢ² = ∫r²dm — Rotational mass. Depends on axis of rotation |
| Torque | τ = r⃗ × F⃗ = rF sin θ — τ in N⋅m. Perpendicular distance × force |
| Rotational Equation of Motion | τ_net = Iα — Torque analogous to force, I to mass, α to acceleration |
| Rotational Kinetic Energy | Ek,rot = ½Iω² — Analogous to ½mv² for translation |
| Angular Momentum | L = Iω, τ_net = dL/dt — Conservation: L = constant if τ_net = 0 |
Gravitation
| Formula | Expression |
|---|---|
| Newton's Law of Gravitation | F = GMm/r² — G = 6.67×10⁻¹¹ N⋅m²/kg². F attractive, always |
| Gravitational Field | g = F/m = GM/r² — g at Earth's surface ≈ 9.8 m/s² or 10 m/s² |
| Gravitational Potential | V = -GM/r — V in J/kg. Potential energy Ep = mV = -GMm/r |
| Escape Velocity | v_esc = √(2GM/R) = √(2gR) — R = planet radius. For Earth ≈ 11.2 km/s |
| Orbital Velocity | v_orb = √(GM/r) = √(gR²/r) — For circular orbit, v_esc = √2 × v_orb |
| Kepler's Third Law | T² ∝ r³ or T² = (4π²/GM)r³ — T = orbital period. Constant for all planets orbiting same star |
Thermodynamics & Kinetic Theory
| Formula | Expression |
|---|---|
| Internal Energy | U = nCvT (ideal gas) — Cv = molar heat capacity at constant volume. U depends only on T |
| First Law of Thermodynamics | ΔU = Q - W — Q = heat added, W = work done by gas. ΔU = change in internal energy |
| Work Done by Gas | W = PΔV (constant pressure), W = nRT ln(Vf/Vi) (isothermal) — W positive if gas expands, negative if compressed |
| Heat Capacity | Q = nCvΔT (const V), Q = nCpΔT (const P) — Cp = Cv + R. For monatomic Cv = (3/2)R, diatomic Cv = (5/2)R |
| Ideal Gas Law | PV = nRT = NkT — R = 8.314 J/(mol⋅K), k = 1.38×10⁻²³ J/K (Boltzmann), N = number of particles |
| Mean Kinetic Energy | ⟨Ek⟩ = (3/2)kT (monatomic) — Average KE of gas molecules. Temperature measure of molecular motion |
| RMS Velocity | v_rms = √(3kT/m) = √(3RT/M) — m = molecular mass, M = molar mass (kg/mol) |
| Entropy Change | ΔS = Q/T (reversible), ΔS = nR ln(Vf/Vi) (isothermal) — S = disorder measure. Second law: ΔS_universe ≥ 0 |
Oscillations & SHM
| Formula | Expression |
|---|---|
| Simple Harmonic Motion | x = A sin(ωt + φ) — A = amplitude, ω = angular frequency, φ = phase. Acceleration a = -ω²x |
| Period & Frequency | T = 2π/ω, f = ω/(2π) = 1/T — T in seconds, f in hertz (Hz) |
| Velocity in SHM | v = ±ω√(A² - x²), v_max = ωA — Velocity maximum at equilibrium, zero at amplitude |
| Energy in SHM | E = ½kA² = ½mω²A² — Total energy constant. E = Ek + Ep at any instant |
| Simple Pendulum | T = 2π√(L/g) — L = length, g = 9.8 m/s². Independent of mass |
| Spring-Mass System | T = 2π√(m/k), ω = √(k/m) — k = spring constant. Period independent of amplitude |
| Damped Oscillations | x = A₀ e^(-t/τ) sin(ωt + φ) — Amplitude decreases exponentially. τ = damping time constant |
Waves
| Formula | Expression |
|---|---|
| Wave Equation | y = A sin(kx - ωt + φ) — k = 2π/λ (wave number), ω = 2πf (angular frequency) |
| Wave Velocity | v = λf = ω/k — λ = wavelength, f = frequency. v = λ × f always |
| Intensity of Wave | I = (1/2)ρvω²A² — I = power per unit area. I ∝ A² (intensity proportional to amplitude squared) |
| Doppler Effect | f' = f(v + v_obs)/(v - v_source) — v = wave velocity. +v when source/observer move closer, -v moving apart |
| Interference Condition | Constructive: Δx = nλ, Destructive: Δx = (n + ½)λ — Δx = path difference, n = 0, 1, 2, ... Two coherent sources required |
| Young's Double Slit | λ = ax/D — a = slit separation, x = fringe width, D = distance to screen |
| Diffraction Minima | b sin θ = nλ (single slit) — b = slit width, θ = diffraction angle, n = 1, 2, 3, ... |
Properties of Matter
| Formula | Expression |
|---|---|
| Density & Relative Density | ρ = m/V, R.D. = ρ_substance / ρ_water — ρ in kg/m³. R.D. dimensionless |
| Stress | Stress = F/A — F = force, A = cross-sectional area. Tensile, compressive, shear stress |
| Strain | Strain = ΔL/L (linear), Strain = ΔV/V (volumetric) — Dimensionless. Change relative to original length/volume |
| Young's Modulus | Y = (F/A)/(ΔL/L) = (stress)/(strain) — Y in Pa (N/m²). Elasticity measure for tension/compression |
| Bulk Modulus | B = -V(ΔP/ΔV) — Resistance to volume change. B in Pa |
| Shear Modulus | η = (F/A)/(Δx/L) = (shear stress)/(shear strain) — η in Pa. Resistance to shape change |
| Surface Tension | T = F/L — F = force, L = length. T in N/m (dyn/cm). Creates surface energy |
| Viscosity | F = ηA(dv/dz) — η = coefficient of viscosity (Pa⋅s). Resistance to flow |
| Stokes' Law | F = 6πηrv — Drag on sphere, radius r, velocity v in viscous medium |
FAQs
What's the difference between average and instantaneous velocity?
Average velocity = total displacement / total time. Instantaneous velocity = velocity at a specific moment (dv/dt). For constant acceleration, average velocity = (initial + final)/2.
How do I solve pulley and incline problems?
Draw free body diagram for each mass separately. Apply Newton's 2nd law (F = ma) to each. For pulleys: if rope doesn't slip, both masses have same acceleration magnitude. For inclines: resolve weight into parallel (mg sin θ) and perpendicular (mg cos θ) components.
When should I use conservation of energy vs work-energy theorem?
Use conservation when no friction/non-conservative forces (Ek₁ + Ep₁ = Ek₂ + Ep₂). Use work-energy when forces act (W_net = ΔEk). For friction problems, W_friction = -μmg×distance, then use work-energy.