Sources of Centripetal Force

19. Static Friction on a Level Curve

When a vehicle travels around a level curve, static friction between its tyres and the road supplies the inward force.

f_s = mv² / r

Friction acts horizontally toward the centre.

Without sufficient friction, the vehicle cannot follow the required circular path.

In real driving, weather, tyre condition and road condition also matter; the ideal equation is not a safety-speed recommendation.

20. Maximum Speed on a Level Curve

The maximum available static friction is:

f_max = μ_s N

On a horizontal road:

N = mg

Therefore:

f_max = μ_s mg

At the limiting condition:

μ_s mg = mv² / r

Cancelling mass:

μ_s g = v²r

Therefore:

v_max = √(μ_s r g)

This is an ideal physics model, not a real-world speed guideline.