Complete Physics Formula Sheet for Class 11 – Chapter-wise Important Formulas

Having a comprehensive formula sheet is essential for Class 11 Physics preparation. This chapter-wise compilation covers all important formulas you need to know for board exams and competitive examinations like JEE and NEET. Bookmark this page for quick revision!

Chapter 1: Physical World and Measurement

Dimensional Formulas

• Force: [MLT⁻²]
• Work/Energy: [ML²T⁻²]
• Power: [ML²T⁻³]
• Pressure: [ML⁻¹T⁻²]
• Momentum: [MLT⁻¹]
• Angular Momentum: [ML²T⁻¹]
• Torque: [ML²T⁻²]

Error Analysis

• Absolute Error: Δa = |a – a_mean|
• Relative Error: δa = Δa/a_mean
• Percentage Error: δa × 100%
• For product/quotient: Δz/z = Δa/a + Δb/b
• For power: Δz/z = n(Δa/a)

Chapter 2: Motion in a Straight Line

Equations of Motion (Constant Acceleration)

• v = u + at
• s = ut + ½at²
• v² = u² + 2as
• s_nth = u + a(2n-1)/2

Average and Instantaneous Values

• Average velocity: v_avg = Δx/Δt = (x₂ – x₁)/(t₂ – t₁)
• Instantaneous velocity: v = dx/dt
• Average acceleration: a_avg = Δv/Δt
• Instantaneous acceleration: a = dv/dt = d²x/dt²

Free Fall

• v = gt (starting from rest)
• h = ½gt²
• v² = 2gh
• Time to reach ground: t = √(2h/g)

Chapter 3: Motion in a Plane

Vector Operations

• |A + B| = √(A² + B² + 2AB cos θ)
• |A – B| = √(A² + B² – 2AB cos θ)
• A · B = AB cos θ = AxBx + AyBy + AzBz
• |A × B| = AB sin θ

Projectile Motion

• Time of flight: T = 2u sin θ / g
• Maximum height: H = u² sin² θ / 2g
• Range: R = u² sin 2θ / g
• Maximum range: R_max = u²/g (at θ = 45°)
• Equation of trajectory: y = x tan θ – gx²/(2u² cos² θ)

Circular Motion

• Angular velocity: ω = θ/t = 2π/T = 2πf
• Linear velocity: v = rω
• Centripetal acceleration: ac = v²/r = ω²r
• Centripetal force: F = mv²/r = mω²r

Chapter 4: Laws of Motion

Newton’s Laws

• First Law: F = 0 implies a = 0
• Second Law: F = ma = dp/dt
• Third Law: F_AB = -F_BA

Friction

• Static friction: f_s ≤ μ_s N
• Kinetic friction: f_k = μ_k N
• Angle of friction: tan φ = μ
• Angle of repose: tan θ = μ_s

Motion on Inclined Plane

• Acceleration down smooth incline: a = g sin θ
• Acceleration down rough incline: a = g(sin θ – μ cos θ)

Chapter 5: Work, Energy and Power

Work

• Work done: W = F · s = Fs cos θ
• Work done by variable force: W = ∫F · ds
• Work-energy theorem: W = ΔKE = ½mv² – ½mu²

Energy

• Kinetic energy: KE = ½mv² = p²/2m
• Potential energy (gravity): PE = mgh
• Potential energy (spring): PE = ½kx²
• Total mechanical energy: E = KE + PE

Power

• Average power: P_avg = W/t
• Instantaneous power: P = dW/dt = F · v
• For constant force: P = Fv cos θ

Chapter 6: System of Particles and Rotational Motion

Center of Mass

• x_cm = Σm_i x_i / Σm_i
• Velocity of CM: v_cm = Σm_i v_i / Σm_i
• Acceleration of CM: a_cm = Σm_i a_i / Σm_i = F_ext / M_total

Moment of Inertia

• I = Σm_i r_i²
• Parallel axis theorem: I = I_cm + Md²
• Perpendicular axis theorem: I_z = I_x + I_y (for planar bodies)

Common Moments of Inertia

• Solid sphere (about diameter): I = (2/5)MR²
• Hollow sphere: I = (2/3)MR²
• Solid cylinder (about axis): I = (1/2)MR²
• Solid disc: I = (1/2)MR²
• Thin rod (about center): I = (1/12)ML²
• Thin rod (about end): I = (1/3)ML²

Rotational Dynamics

• Torque: τ = r × F = rF sin θ
• Angular momentum: L = Iω = r × p
• τ = Iα = dL/dt
• Rotational KE: KE = ½Iω²

Chapter 7: Gravitation

Newton’s Law of Gravitation

• F = Gm₁m₂/r²
• G = 6.67 × 10⁻¹¹ Nm²/kg²

Gravitational Field and Potential

• g at surface: g = GM/R²
• g at height h: g’ = g(1 – 2h/R) for h << R
• g at depth d: g’ = g(1 – d/R)
• Gravitational potential: V = -GM/r
• Gravitational PE: U = -GMm/r

Orbital Motion

• Orbital velocity: v_o = √(GM/r) = √(gR) for near surface
• Escape velocity: v_e = √(2GM/R) = √(2gR)
• Time period: T = 2π√(r³/GM)
• Kepler’s third law: T² ∝ r³

Chapter 8: Mechanical Properties of Solids

Stress and Strain

• Stress = Force/Area = F/A
• Longitudinal strain = ΔL/L
• Young’s modulus: Y = Stress/Strain = FL/AΔL
• Bulk modulus: B = -V(ΔP/ΔV)
• Shear modulus: η = Shear stress/Shear strain

Energy Stored

• Elastic PE per unit volume = ½ × stress × strain
• Elastic PE = ½ × Y × (strain)² × volume

Chapter 9: Mechanical Properties of Fluids

Pressure

• Pressure = Force/Area = F/A
• Pressure at depth: P = P₀ + ρgh
• Pascal’s law: F₁/A₁ = F₂/A₂

Buoyancy

• Buoyant force: F_B = ρ_fluid × V_submerged × g
• Floating condition: ρ_object < ρ_fluid
• Fraction submerged = ρ_object/ρ_fluid

Fluid Dynamics

• Equation of continuity: A₁v₁ = A₂v₂
• Bernoulli’s equation: P + ½ρv² + ρgh = constant
• Torricelli’s theorem: v = √(2gh)

Chapter 10: Thermal Properties of Matter

Temperature Conversion

• C/100 = (F-32)/180 = (K-273)/100
• K = C + 273.15

Thermal Expansion

• Linear: ΔL = αL₀ΔT
• Area: ΔA = βA₀ΔT (β ≈ 2α)
• Volume: ΔV = γV₀ΔT (γ ≈ 3α)

Heat Transfer

• Heat capacity: Q = mcΔT
• Latent heat: Q = mL
• Conduction: Q/t = KA(T₁-T₂)/L
• Stefan’s law: E = σT⁴

Chapter 11: Thermodynamics

First Law

• ΔU = Q – W
• For ideal gas: ΔU = nC_vΔT

Specific Processes

• Isothermal: W = nRT ln(V₂/V₁)
• Adiabatic: PV^γ = constant; TV^(γ-1) = constant
• Isobaric: W = PΔV = nRΔT
• Isochoric: W = 0

Heat Engine Efficiency

• η = W/Q₁ = 1 – Q₂/Q₁
• Carnot efficiency: η = 1 – T₂/T₁

Conclusion

This formula sheet covers the essential formulas for Class 11 Physics. Regular revision of these formulas is crucial for exam success. Remember, understanding the derivation and application of formulas is as important as memorizing them. Practice numerical problems to strengthen your conceptual understanding.