Banked Road and Centripetal Force

Also called

banked road · banking of roads · centripetal force · circular motion · uniform circular motion · friction on a bend · skidding · normal force · angle of banking · tan theta = v squared by rg · cyclist leaning · bending of a cyclist · wall of death · death well · optimum speed · curved road · अभिकेन्द्र बल · वृत्तीय गति · सड़क का ढाल

Topics

• A body moving on a circle needs a centripetal force mv²/r towards the centre; without it, it goes straight on.
• On a flat bend only friction between tyres and road can point towards the centre and supply this force.
• Friction has a limit, μN; if mv²/r needs more than that the car skids outward off its circle.
• A banked road is tilted so the normal force leans inward; its horizontal part provides the centripetal force.
• The vertical part of the normal force balances the weight: N cos θ = mg and N sin θ = mv²/r.
• Dividing the two gives tan θ = v²/rg: at this speed the bend is taken with no help from friction.
• A cyclist leans into a bend so the ground force on the tyres can have an inward part towards the centre.
• On the wall of death the wall's normal force is the whole centripetal force, and friction holds up the weight.

About this model

A GLB file of about 336 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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