# Friction forces on Banked Turns

Published on: Sun Mar 07 2010

Today we talked about the friction force between your car and the tires, which prevents your car from leaving the road. As your wheel rotates it actually has the force of static friction, not kinetic friction, because as wheels rotate they are always in direct contact with the ground except at different points. Only if your wheel stops rotating and continues moving does kinetic friction take over. Friction force can vary, from 0 to μsFn. The Friction force can never exceed the value μsFn. μs depends on the surface. If the curve is flat:

Maximum velocity is equal to the square root of the radius, times gravity, times the static friction component. Now, what happens if this road is banked? Q1: At what angle should a road be tilted so the friction force is not necessary to keep the car on the road?

The angle which makes Friction force unnecessary is the arc tangent of maximum velocity squared divided by gravity times the radius. What happens if you go faster than the design speed?

When driving around a banked curve, and wishing to not fly off it, and going fast enough that if friction force was to vanish you would leave the curve, Maximum velocity is equal to the square root of radius, times gravity times tangent theta plus the coefficient of static friction. Divided by one minus the coefficient of static friction times tangent theta.