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Looking at this picture from Kleppner's mechanics text, Δa is added to $A$ and it is suggested that:

"This causes a change of direction but leaves the magnitude practically unaltered if $ΔA$ is small."

What is practically happening in this sense? When looking at it from a calculus perspective, this makes total sense and the math lines up...but looking at it from a physical perspective my intuition tells me there is some sort of 'stretching' that goes on in the arm/bar/thread that is being rotated via perpendicular force (taking into account friction, a constant force must be needed to maintain uniform velocity).

In a real scenario, what is this 'stretching'? At some point does the arm break? What if we are dealing with the rotation of a particle via an applied field? What is the 'stretching' that goes on here?

user947659
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  • You need to define your terms better. According to the picture it looks like $\Delta A$ is added to $A$. So what is $da/dt$ that you mention in the text? And what exactly is the $r$ that you mention in the question title? Is it the sequence of $A,A',A'',A''',\ldots$ as a function of time? – Cuspy Code Oct 08 '20 at 17:34
  • Somehow you expect the reader to have Kleppers mechanic book at hand. It seems you are talking about circular motion of a arm/bar/thread ? – trula Oct 08 '20 at 17:48
  • @CuspyCode, edited the question to make it consistent. – user947659 Oct 09 '20 at 07:18

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Uniform circular motion dilemma I think this link answers my question and provides some good examples of effects of force as well.

user947659
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