I’m a flying instructor and we teach our students that it is the horizontal component of lift or Centripetal force that turns an aircraft. However, we also teach that this force is balanced by centrifugal force. Now, if turning is a radial acceleration, then surely the forces must be out of balance- Newtons laws!! Can someone explain this to me…??
Properly speaking, a centripetal force is not balanced by a centrifugal force.
Imagine a person sitting in the empty hold of an airplane. When the airplane makes a turn, he’ll slide across the floor, away from the center of the turn, and end up pressed against the wall. There are two different ways to consider this motion.
The centrifugal force is a so-called “fictional” force that only emerges when you consider a rotating frame, e.g. the frame of a person sitting inside the airplane. In that frame, there is no centripetal force. The person in that frame doesn’t accelerate toward the center of the turn, they’re accelerated by the centrifugal force toward the outside of the turn, and end up pressed against the aircraft with a force F[sub]c[/sub]=mv[sup]2[/sup]/r, where m is their mass, v is the plane’s velocity, and r is the radius of the turn.
In a non-rotating frame, we can see that a centripetal force is causing the plane, which normally would go in a straight line because of its inertia, to turn. The passenger feels his own inertia, which tries to make his body move in a straight line, so he slides across the floor, and reaches the wall. The centripetal force on the person is provided by the airplane wall pressing against him, causing him to move on a curved path. This force is given by the same formula: F[sub]c[/sub]=mv[sup]2[/sup]/r. Ultimately this comes from the centripetal force on the airplane itself, which comes from the horizontal component of the lift.
Centripetal and centrifugal forces are equal in size, which might be why your materials are saying that they’re balanced, but from a physics point of view that’s a very sloppy way to put it, because they do not exist in the same frame of reference. They’re just two different ways to think about the same thing: is the passenger pressing against the wall (centrifugal force) or is the wall pressing against the passenger (centripetal force)?
I hope that helps!