📘 Angular Variables
Angular displacement (θ): Angle swept by radius vector. Unit: radian.
Angular velocity (ω): ω = dθ/dt. Related to linear velocity: v = rω.
Angular acceleration (α): α = dω/dt. Tangential acceleration: at = rα.
⚡ Centripetal Acceleration & Force
ac = v²/r = rω². Always directed towards center.
Fc = mv²/r = mrω². Necessary for circular motion.
🎯 Conical Pendulum
T cosθ = mg ; T sinθ = mrω². Period Tp = 2π √(L cosθ / g).
🔁 Vertical Circle
Top: T = mv²/r - mg. Bottom: T = mv²/r + mg. Minimum speed at top: √(gr).
🏦 Banking of Roads
tanθ = v²/(rg). Safe speed on banked road: v = √(rg tanθ).