Lesson 9 of 11 · 11 min
Circular motion
NCERT § "Circular Motion"
On the way home the bus takes a flyover curve of radius 50 m at 10 m/s. Something must be pulling it sideways, towards the centre of the curve, or it would carry straight on. What?
The lesson in notes
In short
Moving at speed v in a circle of radius R, a body has an acceleration v²/R directed towards the centre, so it needs a net force mv²/R towards the centre.
Centripetal force is not a new kind of force; it is supplied by an existing force such as tension, gravity, or friction.
On a level (unbanked) road the centripetal force comes only from static friction between tyres and road, giving a maximum safe speed v_max = √(μ_s R g), independent of the car's mass.
Static friction, not kinetic, is used here because the tyres do not slip sideways on the road.
On a road banked at angle θ, a component of the normal force also points towards the centre, raising the maximum safe speed.
At the optimum speed v₀ = √(R g tan θ) the normal force alone supplies the centripetal force and friction is not needed, which reduces tyre wear.
Below the optimum speed friction acts up the slope; above it, friction acts down the slope.