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Vehicle on flat circular turn
Intermediate
Friction provides centripetal force; maximum speed depends on μ.
v_max = √(μrg)On a flat turn the centripetal force is static friction: μmg ≥ mv²/r, so vmax = √(μrg). Wet roads lower μ and the safe speed.
μ = 0.7, r = 50 m: vmax ≈ 18.5 m/s.
The speed limit doesn't depend on the car's mass.
In more detail
On a flat circular turn, friction provides the centripetal force. The maximum safe speed is set by the coefficient of static friction, v = sqrt(μ r g).
Real-world uses
- Car tyres provide the grip that allows cornering on flat roads.
- Engineers set speed limits on curves based on the available friction.
- A race car taking a corner depends on tyre grip, and the maximum speed rises with the square root of the friction coefficient.
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Frequently asked questions
What happens on ice?
Friction is small, so the maximum speed on a curve drops, and cars may skid outward.
Does mass change the maximum speed?
No, since mass cancels in the friction-limited speed.
Does a heavier car go round a bend faster?
Not in this simple model, because the mass cancels. The limit depends on the friction coefficient and the radius of the bend.
Related topics in Newton's Laws & Forces
Conservation of momentum · Circular motion dynamics · Banking of roads · Conical pendulum · Vertical circular motion · Loop-the-loop