The Coriolis effect is an apparent deflection of moving objects caused by Earth's rotation. It manifests in rotating reference frames and affects any object moving on Earth's surface. Earth rotates at ω = 7.2921×10⁻⁵ rad/s around its polar axis. The Coriolis acceleration is a_c = 2ω × v (vector cross product), where v is velocity and the direction depends on latitude φ. The magnitude a_c = 2ωv sin(φ). At the equator (φ=0°), sin(φ)=0, so there's no Coriolis effect. At poles (φ=90°), sin(φ)=1, maximum effect. This directional variation explains why hurricanes spin counterclockwise in Northern Hemisphere and clockwise in Southern Hemisphere. The effect is crucial in meteorology—storm systems are deflected, atmospheric circulation patterns form, and weather prediction requires accounting for Coriolis deflection. In oceanography, ocean currents spiral (Ekman spiral) due to Coriolis effect interacting with wind stress. Deflection distance scales with velocity and duration; a 100 m/s wind at 50° latitude deflects approximately 150-200 meters over 1000 km due to Coriolis. Fast-moving objects (jets, missiles, artillery) experience significant deflection. At low velocities, deflection is negligible. The effect is independent of object mass—a feather deflects identically to a cannonball at same velocity. Historical significance: Coriolis effect explained by Gaspard-Gustave Coriolis (1835); initially questioned, now fundamental to geophysics. Modern applications: missile guidance systems, weather forecasting, oceanographic models, aircraft navigation.

Mathematical framework: in rotating frame, fictitious forces include centrifugal and Coriolis. For projectile motion with time t, lateral deflection ≈ (1/3)ωv t³ for small angles. At latitude 45°, a 50 m/s object experiences 7.27×10⁻⁵ m/s² acceleration; over 1000 km (20,000 seconds), deflection ~146 meters. Coriolis force is always perpendicular to motion velocity, never doing work. Calculation requires 3D vector analysis; in 2D approximations (flat Earth models), vertical component ignored for practical applications. Meteorological implications: isobars (constant pressure contours) align with geostrophic wind (wind balanced between pressure gradient and Coriolis). Wind speeds ~10-20 m/s; strong storms intensify due to this balance. Inertial oscillations occur when pressure gradient removed—objects circle at inertial period T = 2π/f = 24 hours/sin(φ). At equator, period infinite (no oscillation); at poles, 12-hour cycles (half pendulum day). Practical applications: weather prediction models must include Coriolis parameter f = 2ω sin(φ); omission causes forecast errors within 24 hours. Hurricane forecasting, typhoon tracking, cyclone warnings all depend on Coriolis calculations. Modern meteorological software uses f-plane approximation (constant locally) or β-plane (latitude-dependent) for computational efficiency.