Turns

A turn is basically the term for when an object moves circularly around a given axis or point.

In a turn, banked or not, three key forces act on the object turning: static friction, gravity, and normal force. In fact, on a regular turn, friction is the centripetal force required to keep the object turning at its given radius. If the object turns at too high of a speed(known as turning too hard), their curvature will cave in. This is important to know for any type of circular motion and it usually relates with the speed of the object because that's the most variable quantity in the equation for centripetal force. If the speed is too high, the object will trail away, if the speed is too low, the object will cave in, and if the velocity is just right, the object will stay on its circular path.

An unbanked turn is very simple in its circular mechanics. Let's use a car for example. For a car, the centripetal force acting on the car is just static friction between the road and itself. The net vertical force is zero as the normal force and weight vectors on the car cancel out entirely. Keep in mind that there is no outward force acting on someone in this car from a stationary external observer; it's just their inertia. However, inside the car, the inertial force of centrifugal force acts outward on a passenger.

The vertical forces on the car are just the normal force on it and its weight. Since the car doesn't move up or down while turning, we can deduce that its vertical acceleration, and thus force, is 0.

The only centripetal force acting on this car during the unbanked turn is static friction. This acts radially left if the car turns left and radially right if the car turns right.

The maximum speed of an object on an unbanked turn is given by:

This is good to know because it helps realize that ultimately, the radius decides the variation in speed from different turn designs. The coefficient of fraction(static) and gravity won't change but radius can.

Banked turns with no friction are very different from unbanked turns because now the normal force acts at noticeable angles relative to the radius of curvature. This means we have to starts splitting force vectors into components. However, the same three forces act in essentially the same 3 ways for objects on banked turns.

The equation above is the maximum speed an object can have given these parameters in the equation. Since normal force is the only force providing some centripetal force, the angle is important because that dictates how much normal force is pulling the object in during the banked turn.