rudderrudderrat:
There is no mention of TAS in equation (1)
You're going to have to actually listen to what I say. What is the equation for THP? You'll find that TAS is in that equation.
... the ball is in an inertial frame of reference - not you.
As I've said before, being on the earth puts you in an accelerating reference frame (non-inertial reference frame). However, you can analyze a number of phenomena by treating it as an inertial reference frame. Some of these include your golf ball example and an aircraft in flight. Go take a physics course.
I sincerely hope that you do not confuse your students with the theory of General Relativity, whilst explaining what a simple balanced turn is all about.
I don't think you understand the difference between proving and explaining. I do not start by proving what frame of reference we're in and then proving all the forces and so on. You would need to be enrolled in an advanced physics course to begin down that path.
I start by explaining the forces in a turn by drawing something like this:
http://selair.selkirk.ca/Training/Ae...es/lf-turn.gif
This picture is wrong:
http://www.aero-mechanic.com/wp-cont...09/08/4-28.jpg
It shows the forces from an inertial reference frame and a non-inertial reference frame. As I've shown before, if the forces are equal, there is no acceleration. So how does the aircraft turn if the forces are actually balanced, like shown in the second picture?
I usually don't mention how forces in a turn are sometimes depicted incorrectly. But I have the knowledge to be able to answer questions regarding the forces in a turn if the student asks.