Centripetal Force: F_c = mv²/r = mω²r is the net force toward the center that keeps an object in circular motion. Not a new force type - it's the result of real forces (tension, friction, gravity, normal force) acting toward the center. Always perpendicular to velocity.
Centripetal Acceleration: a_c = v²/r = ω²r = 4π²r/T². Direction changes continuously (always toward center), causing velocity direction to change even at constant speed. Measured in m/s².
Period & Frequency: Period T = 2πr/v = 2π/ω (seconds per revolution). Frequency f = 1/T = v/(2πr) (revolutions per second, Hz). Angular velocity ω = v/r = 2π/T = 2πf (rad/s).
Banking Angle: tan(θ) = v²/(rg). Banked curves allow turning without friction by tilting the normal force toward the center. Race tracks: steep banking (30-45°). Highways: gentle banking (3-5°).
Vertical Circles: At top: T + mg = mv²/r (minimum speed v = √(gr) to maintain contact). At bottom: T - mg = mv²/r (maximum tension). Roller coaster loops use this principle.
Applications: Car turning (friction provides F_c), satellites orbiting (gravity provides F_c), washing machine spin cycle, centrifuges, amusement park rides, planetary motion, sports (hammer throw, velodrome cycling).