Classical & Modern Physics Fundamentals

Physics spans CM, EM, thermo, QM, and SR/GR. Understanding requires both mathematical rigor and physical intuition for real-world application.

## Classical Mechanics

Newton's Laws form the foundation: N1 (inertia) — object at rest stays at rest unless acted on by net external force. N2: F=ma (vector equation, apply component-wise). N3: action-reaction pairs act on DIFFERENT bodies (common misconception: they don't cancel). Weight W=mg where g=9.81 m/s² (varies w/ altitude and latitude).

Kinematics (constant accel): v = v₀ + at, x = x₀ + v₀t + ½at², v² = v₀² + 2a(x-x₀). Projectile motion: decompose into independent x (ax=0) and y (ay=-g) components. Range R = v₀²sin(2θ)/g, max at θ=45°. Air resistance makes real trajectories asymmetric.

Energy methods often simpler than force analysis. KE = ½mv², gravitational PE = mgh (near surface), elastic PE = ½kx². Work-energy theorem: Wnet = ΔKE. Conservation of energy: if only conservative forces act, Ei = Ef. Power P = dW/dt = F·v.

Momentum: p = mv (vector). Impulse J = FΔt = Δp. Conservation of momentum in isolated systems. Collisions: elastic (KE conserved) vs inelastic (KE not conserved). Perfectly inelastic → objects stick together, max KE loss. COM velocity unchanged in all collision types.