Re: Instantaneous radius of a rotation

But it is unnecessary. If the trajectory is u(t), the
acceleration is u"(t), and the required force is mu"(t) . The reaction
(centrifugal) force is just opposite this.

Is that what you were after?

You are right. But this is only the magnitude of the force.

Imagine that we have an aircraft, it's nose is pointing in the sky
(e.g. pitch angle of 10 degrees) and it starts to bank for a turn.

The question is:

What is the direction vector of the centrifugal force ?

.

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