Physics — Formula Sheet
All key formulas for TS Inter 1st Year Physics — 14 chapters from the official TGBIE Annual Plan 2025-26. Chapter-wise for quick revision.
Ch. 2 Units and Measurements
- 1% error = (ΔA/A) × 100
- 2Combination errors: A+B → ΔZ = ΔA + ΔB; A×B → ΔZ/Z = ΔA/A + ΔB/B
- 3Dimensional formula key: [F] = MLT⁻², [E] = ML²T⁻², [P] = ML⁻¹T⁻², [Power] = ML²T⁻³
Ch. 3 & 4 Motion in a Straight Line & Plane
- 1v = u + at; s = ut + ½at²; v² = u² + 2as; s_n = u + a(2n−1)/2
- 2Projectile: Time of flight T = 2u·sinθ/g; Range R = u²·sin2θ/g; Max height H = u²·sin²θ/(2g)
- 3Max range: θ = 45°, R_max = u²/g
- 4Relative velocity: v_AB = v_A − v_B
Ch. 5 Laws of Motion
- 1Newton's 2nd law: F = ma
- 2Friction: f_s ≤ μ_s·N; f_k = μ_k·N (kinetic)
- 3Banking angle: tanθ = v²/(rg)
- 4Impulse: J = FΔt = Δp
Ch. 6 Work, Energy and Power
- 1Work: W = F·d·cosθ
- 2KE = ½mv²; PE = mgh (gravitational)
- 3Work-energy theorem: W_net = ΔKE
- 4Power: P = W/t = F·v
- 5Elastic collision: v₁' = (m₁−m₂)u₁/(m₁+m₂) + 2m₂u₂/(m₁+m₂)
- 6Perfectly inelastic: v = (m₁u₁+m₂u₂)/(m₁+m₂)
Ch. 7 System of Particles and Rotational Motion
- 1Torque: τ = r × F = Iα
- 2Moment of Inertia: I = Σmᵢrᵢ²
- 3Angular momentum: L = Iω; L = mvr
- 4Parallel axis: I = I_cm + md²
- 5Perpendicular axis: I_z = I_x + I_y (for laminar bodies)
- 6Rolling without slipping: v_cm = Rω; KE = ½mv² + ½Iω²
- 7Rod about centre: I = ML²/12; about end: I = ML²/3
- 8Disc/cylinder about axis: I = MR²/2; Sphere about diameter: I = 2MR²/5
Ch. 8 Oscillations (SHM)
- 1x = A·sin(ωt + φ); ω = 2π/T = 2πf
- 2v = ω√(A²−x²); a = −ω²x
- 3Energy: KE = ½mω²(A²−x²); PE = ½mω²x²; Total E = ½mω²A²
- 4Simple pendulum: T = 2π√(L/g)
- 5Spring-mass: T = 2π√(m/k)
Ch. 9 Gravitation
- 1F = Gm₁m₂/r²; G = 6.67 × 10⁻¹¹ N·m²/kg²
- 2g = GM/R²; g at height h: g_h = g(1 − 2h/R) (h << R)
- 3g at depth d: g_d = g(1 − d/R)
- 4Orbital velocity: v_o = √(GM/r) = √(gR²/r)
- 5Escape velocity: v_e = √(2gR) = √(2GM/R) ≈ 11.2 km/s for Earth
- 6Time period of satellite: T = 2π√(r³/GM)
- 7Gravitational PE: U = −GMm/r
Ch. 10 & 11 Mechanical Properties
- 1Stress = F/A; Strain = ΔL/L (longitudinal)
- 2Young's modulus: Y = Stress/Strain = FL/(AΔL)
- 3Bulk modulus: B = −V·ΔP/ΔV
- 4Pressure: P = ρgh; Absolute P = P₀ + ρgh
- 5Continuity: A₁v₁ = A₂v₂
- 6Bernoulli: P + ½ρv² + ρgh = constant
- 7Surface tension: T = F/L; excess pressure in bubble = 4T/r
- 8Stokes law: F = 6πηrv; terminal velocity: v_t = 2r²(ρ−σ)g/(9η)
Ch. 12, 13, 14 Thermal Properties, Thermodynamics, Kinetic Theory
- 1Linear expansion: ΔL = αLΔT; Volume: ΔV = γVΔT; γ = 3α
- 2Q = mcΔT (sensible heat); Q = mL (latent heat)
- 3PV = nRT (ideal gas); n = number of moles
- 41st law: ΔU = Q − W
- 5Isothermal: W = nRT·ln(V₂/V₁); Adiabatic: PV^γ = constant
- 6Efficiency of Carnot engine: η = 1 − T₂/T₁ = (T₁−T₂)/T₁
- 7KE per molecule = (3/2)kT; k_B = 1.38 × 10⁻²³ J/K
- 8rms speed: v_rms = √(3kT/m) = √(3RT/M)
- 9Mean free path: λ = kT/(√2·πd²P)