Complete formula sheet for CBSE Class 11 Physics. Covers mechanics, thermodynamics, waves, and properties of matter. SI units throughout.
[M^a L^b T^c I^d K^e]M = mass, L = length, T = time, I = current, K = temperature, N = amount of substanceLength (m), Mass (kg), Time (s), Current (A), Temperature (K)SI base units. Derived units combine these: velocity (m/s), force (N=kg⋅m/s²)Δx/x = ±(Δa/a + Δb/b) for products/quotientsPercentage error = (Δx/x)×100%. Random errors reduce with multiple measurements.s = x₂ - x₁ (vector), distance = |s| (scalar)Displacement can be negative (change in position)v = ds/dt, a = dv/dt = d²s/dt²Average: v_avg = Δs/Δt, a_avg = Δv/Δtv = u + atLinear motion, constant accelerations = ut + ½at²Displacement formulav² = u² + 2asConnects velocity, acceleration, displacementx = v₀ₓt, y = v₀ᵧt - ½gt², tan θ = v₀ᵧ/v₀ₓx-axis: uniform, y-axis: uniformly accelerated (g = 10 m/s²)R = v₀² sin 2θ / g, H = v₀² sin² θ / (2g)R maximum at θ = 45°. H for vertical component only.F_net = 0 → a = 0 (equilibrium)Object at rest/uniform motion stays so unless net force actsF_net = ma → a = F_net/mF in newtons (N), m in kg, a in m/s²F_AB = -F_BAAction-reaction forces are equal, opposite, on different objectsf_s ≤ μ_s N, f_k = μ_k Nμ_s = static friction coefficient, μ_k = kinetic, N = normal forceW = mg, N = mg cos θ (on incline)Weight always downward, normal force perpendicular to surfaceT = ma + mg (for acceleration upward)Free body diagram essential. For pulley systems, use F_net on each mass.W = F⃗ · s⃗ = Fs cos θW in joules (J). Positive: force in direction of motion, Negative: against motionEk = ½mv²Energy due to motion. KE always ≥ 0Ep = mghRelative to reference level. Change in PE = mg(h₂ - h₁)W_net = ΔEk = ½m(v₂² - v₁²)Net work equals change in kinetic energyE_total = Ek + Ep = constant (no friction)Mechanical energy conserved in isolated systemsP = W/t = Fv cos θP in watts (W). Average vs instantaneous powerEp = ½kx²k = spring constant (N/m), x = extension (m)θ = s/r (in radians)s = arc length, r = radius. 1 radian = 57.3°, 2π rad = 360°ω = dθ/dt, v = rωω in rad/s. Linear velocity v at circumferenceα = dω/dt, a_t = rαα in rad/s². a_t = tangential accelerationa_c = v²/r = ω²rDirected toward center. Always perpendicular to velocityI = Σmᵢrᵢ² = ∫r²dmRotational mass. Depends on axis of rotationτ = r⃗ × F⃗ = rF sin θτ in N⋅m. Perpendicular distance × forceτ_net = IαTorque analogous to force, I to mass, α to accelerationEk,rot = ½Iω²Analogous to ½mv² for translationL = Iω, τ_net = dL/dtConservation: L = constant if τ_net = 0F = GMm/r²G = 6.67×10⁻¹¹ N⋅m²/kg². F attractive, alwaysg = F/m = GM/r²g at Earth's surface ≈ 9.8 m/s² or 10 m/s²V = -GM/rV in J/kg. Potential energy Ep = mV = -GMm/rv_esc = √(2GM/R) = √(2gR)R = planet radius. For Earth ≈ 11.2 km/sv_orb = √(GM/r) = √(gR²/r)For circular orbit, v_esc = √2 × v_orbT² ∝ r³ or T² = (4π²/GM)r³T = orbital period. Constant for all planets orbiting same starU = nCvT (ideal gas)Cv = molar heat capacity at constant volume. U depends only on TΔU = Q - WQ = heat added, W = work done by gas. ΔU = change in internal energyW = PΔV (constant pressure), W = nRT ln(Vf/Vi) (isothermal)W positive if gas expands, negative if compressedQ = nCvΔT (const V), Q = nCpΔT (const P)Cp = Cv + R. For monatomic Cv = (3/2)R, diatomic Cv = (5/2)RPV = nRT = NkTR = 8.314 J/(mol⋅K), k = 1.38×10⁻²³ J/K (Boltzmann), N = number of particles⟨Ek⟩ = (3/2)kT (monatomic)Average KE of gas molecules. Temperature measure of molecular motionv_rms = √(3kT/m) = √(3RT/M)m = molecular mass, M = molar mass (kg/mol)ΔS = Q/T (reversible), ΔS = nR ln(Vf/Vi) (isothermal)S = disorder measure. Second law: ΔS_universe ≥ 0x = A sin(ωt + φ)A = amplitude, ω = angular frequency, φ = phase. Acceleration a = -ω²xT = 2π/ω, f = ω/(2π) = 1/TT in seconds, f in hertz (Hz)v = ±ω√(A² - x²), v_max = ωAVelocity maximum at equilibrium, zero at amplitudeE = ½kA² = ½mω²A²Total energy constant. E = Ek + Ep at any instantT = 2π√(L/g)L = length, g = 9.8 m/s². Independent of massT = 2π√(m/k), ω = √(k/m)k = spring constant. Period independent of amplitudex = A₀ e^(-t/τ) sin(ωt + φ)Amplitude decreases exponentially. τ = damping time constanty = A sin(kx - ωt + φ)k = 2π/λ (wave number), ω = 2πf (angular frequency)v = λf = ω/kλ = wavelength, f = frequency. v = λ × f alwaysI = (1/2)ρvω²A²I = power per unit area. I ∝ A² (intensity proportional to amplitude squared)f' = f(v + v_obs)/(v - v_source)v = wave velocity. +v when source/observer move closer, -v moving apartConstructive: Δx = nλ, Destructive: Δx = (n + ½)λΔx = path difference, n = 0, 1, 2, ... Two coherent sources requiredλ = ax/Da = slit separation, x = fringe width, D = distance to screenb sin θ = nλ (single slit)b = slit width, θ = diffraction angle, n = 1, 2, 3, ...ρ = m/V, R.D. = ρ_substance / ρ_waterρ in kg/m³. R.D. dimensionlessStress = F/AF = force, A = cross-sectional area. Tensile, compressive, shear stressStrain = ΔL/L (linear), Strain = ΔV/V (volumetric)Dimensionless. Change relative to original length/volumeY = (F/A)/(ΔL/L) = (stress)/(strain)Y in Pa (N/m²). Elasticity measure for tension/compressionB = -V(ΔP/ΔV)Resistance to volume change. B in Paη = (F/A)/(Δx/L) = (shear stress)/(shear strain)η in Pa. Resistance to shape changeT = F/LF = force, L = length. T in N/m (dyn/cm). Creates surface energyF = ηA(dv/dz)η = coefficient of viscosity (Pa⋅s). Resistance to flowF = 6πηrvDrag on sphere, radius r, velocity v in viscous medium