Free Physics Formulas Guide: Solve Problems Faster with These Formulas

Free Physics Formulas: Essential Equations for Students and Engineers

Physics reduces the complexity of the natural world to concise equations. Whether you’re a student preparing for exams or an engineer designing systems, having a compact set of essential formulas at hand speeds problem solving and improves intuition. Below is a focused, organized reference covering core areas: mechanics, waves & optics, thermodynamics, electromagnetism, and modern physics. Each section lists key formulas, a short explanation of variables, and quick notes on common use or units.

Mechanics — Motion, Forces, Energy

• Newton’s Second Law: F = ma
  Variables: F (force, N), m (mass, kg), a (acceleration, m/s²).
  Note: Vector equation; apply separately per axis.

• Kinematic (constant acceleration): v = v0 + at
  Variables: v (final velocity), v0 (initial velocity), a (acceleration), t (time).

• Displacement (constant acceleration): s = s0 + v0 t + ½ a t²

• Kinematic relation (no time): v² = v0² + 2a(s − s0)

• Work: W = F · d = F d cosθ
  Units: Joules (J). Work = area under force–displacement.

• Kinetic Energy: KE = ½ m v²

• Gravitational Potential Energy (near Earth): U = m g h
  g ≈ 9.81 m/s².

• Power: P = dW/dt = F v

• Momentum: p = m v
  Conservation: p_initial = p_final (closed system).

• Impulse: J = Δp = F_avg Δt

Rotational Dynamics

• Angular velocity and acceleration: ω = dθ/dt, α = dω/dt

• Relation to linear motion: v = ω r, a_tangential = α r

• Moment of inertia (common shapes):

  • Solid cylinder (axis): I = ½ m r²
  • Solid sphere (axis): I = ⁄₅ m r²
  • Thin rod (center): I = ⁄₁₂ m L²

• Torque: τ = r × F = I α

• Rotational kinetic energy: KE_rot = ½ I ω²

Gravitation & Orbits

• Newton’s law of universal gravitation: F = G m1 m2 / r²
  G ≈ 6.674×10⁻¹¹ N·m²/kg².

• Gravitational potential energy (two masses): U = −G m1 m2 / r

• Orbital velocity (circular): v = √(G M / r)

• Escape velocity: v_escape = √(2 G M / r)

Waves & Optics

• Wave speed: v = f λ
  Variables: f (frequency), λ (wavelength).

• Simple harmonic motion (mass–spring): ω = √(k/m)
  Period: T = 2π √(m/k)

• String/pipe harmonics (example for string fixed at both ends): λ_n = 2L/n

• Snell’s Law (refraction): n1 sinθ1 = n2 sinθ2

• Lensmaker’s formula (thin lens): 1/f = 1/do + 1/di

Thermodynamics & Statistical Basics

• Ideal gas law: PV = n R T = N k_B T
  R = 8.314 J/(mol·K), k_B = 1.381×10⁻²³ J/K.

• First law (energy conservation): ΔU = Q − W
  Sign conventions: Q into system positive, W done by system positive.

• Work for quasi-static isothermal process (ideal gas): W = n R T ln(Vf/Vi)

• Heat capacity (constant volume): Cv = (∂U/∂T)_V

• Entropy change (reversible): dS = δQ_rev / T

Electricity & Magnetism

• Coulomb’s law: F = k q1 q