Why does the plane yaw when the rate of turn is not suitable to bank angle in a turn? In a slipping/skidding turn, there is an imbalance of centripetal/ centrifugal force. How does that cause a yaw?
Why does the plane yaw when the rate of turn is not suitable to bank angle in a turn?
If you mean why does the plane slip or skid when the rate of turn is not suitable to bank angle in a turn, then see item #5 below.
In a slipping/skidding turn, there is an imbalance of centripetal/ centrifugal force. How does that cause a yaw?
It really doesn't.
Here's a better way to think about slip and skids and the resulting imbalance in forces--
The "causal chain" goes like this--
- Airplane nose is not fully aligned, yaw-wise, with actual instantaneous direction of travel, generally due to some aerodynamic yaw torque (for example due to "adverse yaw" from the deflected ailerons and/or from a non-zero roll rate, or due to an intentional rudder input by the pilot) that counteracts the aircraft's natural "weathervane stability" or "directional stability". Yaw rotational inertia can also play a contributing role as a turn is being initiated (or exited), but this effect is generally slight.
(This "misalignment" between nose and instantaneous direction of flight path is sort of but not exactly the same as the yaw rate being "wrong" for the bank angle.)
Side of fuselage is exposed to free-stream relative wind
Airflow hits side of fuselage and generates a real, tangible aerodynamic force
The net aerodynamic force vector is no longer pointing straight "up" in the reference frame of the banked aircraft, as it would be if the wings' lift vector were the only unbalanced aerodynamic force at play.
This causes a reduction (or increase) in turn rate so the turn rate is now "too low" (or "too high") for the bank angle.
This also causes the slip-skid ball to ride off-center.
Note that either item 4 or item 5 can be viewed as the fundamental "cause" of item 6, depending what reference frame we use. Item 4 rather than item 5 is best viewed as the cause of item 6 if we are using a valid inertial reference frame -- e.g. the earth, not the moving airplane-- in which case our explanation should not invoke the fictitious "centrifugal force".
Note that for the exact same degree of "misalignment" between the aircraft nose and the actual instantaneous direction of the flight path-- i.e. the exact same displacement of a "yaw string"-- the resulting amount of aerodynamic sideforce generated by the airflow against the fuselage, and the resulting displacement of the slip-skid ball, and the resulting change in the turn rate, will vary according to the shape of the fuselage and the amount of side area therefore presented to the airflow. So a given deflection of the yaw string will cause a different deflection of the slip-skid ball in various different aircraft.
Note that by putting item #1 at the very front of the "causal chain", we're well equipped to understand why appropriate rudder inputs are the key to preventing slips and skids.
Note also that this perspective works well even for extreme cases, even including 90-degree-banked "knife edge" linear flight such as we see at airshows. Some other "explanations" that we read in pilot training materials tend to break down in such extreme cases.