Physics Formula Sheet
1. UNITS AND DIMENSIONS
- Dimensional Formulae [Length] = [L] [Mass] = [M] [Time] = [T] [Velocity] = [LT⁻¹] [Acceleration] = [LT⁻²] [Force] = [MLT⁻²] [Momentum] = [MLT⁻¹] [Pressure] = [ML⁻¹T⁻²] [Energy] = [ML²T⁻²] [Power] = [ML²T⁻³]
2. KINEMATICS (1D)
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- s = (u + v)t / 2
- Average velocity = Total displacement / Total time
- Instantaneous velocity v = lim Δt→0 (Δs/Δt) = ds/dt
- Acceleration a = dv/dt = d²s/dt²
3. LAWS OF MOTION
- Newton’s First Law: ΣF⃗ = 0 (For rest or uniform motion)
- Newton’s Second Law: ΣF⃗ = dp⃗/dt = ma⃗
- Newton’s Third Law: F⃗₁₂ = −F⃗₂₁
- Weight: W = mg
- Friction: fₛ ≤ μₛN, fₖ = μₖN
4. WORK, ENERGY & POWER
- Work: W = F⃗ · s⃗ = Fs cos θ
- Kinetic Energy: K = ½mv²
- Potential Energy: U = mgh
- Work–Energy Theorem: Wnet = ΔK = Kf − Ki
- Power: P = dW/dt = Fv cos θ
- Energy is conserved if only conservative forces act.
5. SYSTEM OF PARTICLES & ROTATIONAL MOTION
- Centre of Mass: R⃗CM = Σmᵢr⃗ᵢ / Σmᵢ
- Momentum: p⃗ = Σp⃗ᵢ = MVCM
- Torque: τ⃗ = r⃗ × F⃗ ; τ = rF sin θ
- Angular Momentum: L⃗ = r⃗ × p⃗
- Moment of Inertia: I = Σmᵢrᵢ² (discrete) I = ∫r²dm (continuous)
- Rotational Motion: τ = Iα α = dω/dt
- Angular Kinematics: ω = ω₀ + αt θ = ω₀t + ½αt² ω² = ω₀² + 2αθ
6. GRAVITATION
- Universal Law: F = Gm₁m₂/r²
- Acceleration due to gravity: g = GM/R²
- Gravitational Potential: V = −GM/r
- Escape Velocity: vₑ = √(2GM/R)
- Orbital Velocity: v = √(GM/r)
7. PROPERTIES OF MATTER
- Density: ρ = m/V
- Relative Density: R.D. = ρsubstance/ρwater
- Pressure: P = F/A
- Pascal’s Law: F₁/A₁ = F₂/A₂
- Archimedes’ Principle: Fb = ρfgVdisplaced
8. THERMAL PROPERTIES OF MATTER
- Heat: Q = mcΔT
- Specific Heat Capacity: c = Q/(mΔT)
- Latent Heat: Q = mL
- Ideal Gas Equation: PV = nRT
- Work done by gas: W = ∫V₁V₂P dV
9. OSCILLATIONS
- SHM Equation: x = A sin(ωt + φ)
- Velocity: v = dx/dt = ω√(A² − x²)
- Acceleration: a = d²x/dt² = −ω²x
- Time Period: T = 2π√(m/k)
- Frequency: f = 1/T = (1/2π)√(k/m)
- Energy in SHM: E = ½kA²
10. WAVES
- Wave Speed: v = fλ
- Displacement: y = A sin(ωt − kx + φ)
- Wave Number: k = 2π/λ
- Angular Frequency: ω = 2πf
- Intensity: I = P/A ∝ A²
- Superposition Principle applies.
11. ELECTROSTATICS
- Coulomb’s Law: F = (1/4πε₀) q₁q₂/r²
- Electric Field: E⃗ = q⃗₀/(4πε₀r²)
- Electric Flux: Φ = E⃗ · A⃗ = EA cos θ
- Gauss’ Law: ∮E⃗ · dA⃗ = qencl/ε₀
- Potential: V = (1/4πε₀)q/r
- Capacitance: C = Q/V
12. CURRENT ELECTRICITY
- Ohm’s Law: V = IR
- Resistance: R = ρL/A
- Resistivity: ρ = RA/L
- Power: P = VI = I²R = V²/R
- In Series: Req = R₁ + R₂ + ...
- In Parallel: 1/Req = 1/R₁ + 1/R₂ + ...
13. MAGNETISM
- Force on charge: F⃗ = q(v⃗ × B⃗)
- Force on current element: dF⃗ = I(dℓ⃗ × B⃗)
- Magnetic Field (Biot–Savart Law): dB⃗ = μ₀/(4π) · I(dℓ⃗ × r̂)/r²
- Ampere’s Law: ∮B⃗ · dℓ⃗ = μ₀Iencl
- Lorentz Force: F⃗ = q(E⃗ + v⃗ × B⃗)
14. MODERN PHYSICS
- Photoelectric Equation: hν = φ + Kmax
- de Broglie Wavelength: λ = h/p = h/mv
- Planck’s Relation: E = hν
- Mass–Energy Equivalence: E = mc²
IMPORTANT CONSTANTS
μ₀ = 4π × 10⁻⁷ T·m·A⁻¹ | g = 9.8 m s⁻² | G = 6.67 × 10⁻¹¹ N m² kg⁻² | ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻²
h = 6.626 × 10⁻³⁴ J s | c = 3 × 10⁸ m s⁻¹
μ₀ = 4π × 10⁻⁷ T·m·A⁻¹ | g = 9.8 m s⁻² | G = 6.67 × 10⁻¹¹ N m² kg⁻² | ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻²
h = 6.626 × 10⁻³⁴ J s | c = 3 × 10⁸ m s⁻¹