Fluids
P = F/A = P₀ + ρgh | F_buoyant = ρ_fluid × V_displaced × g
Bernoulli's principle and Venturi effect
Bernoulli: P + ½ρv² + ρgh = constant | Continuity: A₁v₁ = A₂v₂
Key Point: Narrower tube → faster flow → lower pressure. Clinical: aneurysm (wider = higher P), stenosis (narrower = lower P, faster flow).
Circuits
Series vs parallel circuits
V = IR | P = IV = I²R = V²/R
| Series | Parallel |
|---|
| Current | Same (I) | Splits (I = I₁ + I₂) |
| Voltage | Splits (V = V₁ + V₂) | Same (V) |
| Resistance | R = R₁ + R₂ | 1/R = 1/R₁ + 1/R₂ |
| Capacitance | 1/C = 1/C₁ + 1/C₂ | C = C₁ + C₂ |
Optics
Converging lens image formation
1/f = 1/dₒ + 1/dᵢ | M = −dᵢ/dₒ = hᵢ/hₒ
Snell's law: n₁ sin θ₁ = n₂ sin θ₂
Key Point: Converging lens/concave mirror: f > 0. Diverging lens/convex mirror: f < 0. Real images: dᵢ > 0. Virtual: dᵢ < 0.
Waves & EM Spectrum
The electromagnetic spectrum
v = fλ | E = hf = hc/λ | c = 3 × 10⁸ m/s