Car on a Curve

This interactive simulator explores Car on a Curve in Classical Mechanics. Flat: v_max = √(μgR), F_c vs μmg. Banked ideal: tan θ = v²/(gR). Top view + wedge. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Classical Mechanics.

Key terms

  • car
  • curve
  • car on curve
  • mechanics
  • classical

Live graphs

How it works

Horizontal flat turn: lateral acceleration v²/R must be provided by friction, with maximum μₛmg, so v_max = √(μₛgR). Banked frictionless turn: the normal force’s horizontal component supplies centripetal acceleration, giving the design condition tan θ = v²/(gR). This complements Circular Motion (string tension) with road friction and banking.

Key equations

Flat:   mv²/R ≤ μₛmg  ⇒  v ≤ √(μₛgR)
Banked (no friction):   N sin θ = mv²/R, N cos θ = mg  ⇒  tan θ = v²/(gR)