Circular Motion · Interactive

Banking & Circular Motion

Take a car around a banked curve and find the fastest safe speed before it skids. Tilt the road, add friction, and watch the normal force, friction and the required centripetal pull rebalance — or flip to a conical pendulum swinging the same physics on a string.

Normal N Friction f Centripetal Weight mg Cross-section + top-down track

Setup

Radius r 50 m
Bank angle θ 20 °
Friction μ 0.30
Speed v 18 m/s
Car mass m 1200 kg
Safe
Grip state
needed F_c (kN)
v_max (m/s)
v_min (m/s)
ideal v₀ (m/s)
F_c = mv²/r v_max = √(rg(tanθ+μ)/(1−μtanθ)) ideal tanθ = v²/rg

Playback

Try this: raise the bank angle and the safe-speed window widens — at exactly the ideal speed v₀ you need no friction at all (the friction arrow vanishes). Push past v_max and the track turns red as the car skids outward.