Minimum-speed case: friction points up the slope. Fc is the Available inward force.
This interactive 3D physics simulation demonstrates circular motion on a banked track. Students can explore how the normal force, friction, weight, and inward net force determine the maximum speed of a car moving around a curve.
In circular motion, the centripetal force is the Available inward force. It is not an additional force placed on the force diagram. For a car on a banked track, the real forces are weight, normal force, and friction.
For the minimum-speed case, the car tends to slide down the bank, so friction acts up the slope. The inward net force is the inward component of the normal force minus the outward component of friction.
Using vertical equilibrium and f = μN:
The normal force is perpendicular to the banked road surface and has both vertical and inward components.
At maximum speed, friction acts down the slope and contributes an inward component.
The inward components of real forces provide the centripetal acceleration.
The maximum speed depends on the curve radius, bank angle, gravitational acceleration, and coefficient of friction.