# Problem in understanding in the derivation of torsion acting on a circular shaft fixed at one end

My doubt is how Arc(ab) = L $\gamma$. Arc (ab) = R$\theta$ makes sense as that's the arc of that circle.

• Because $\gamma$ is a small angle. – lucas Jun 3 '16 at 10:48

If the angle $\gamma$ is small we can approximate the arc $AB$ as a straight line:
Then the length $AB$ is simply:
$$AB = L\tan\gamma$$
Since $\gamma$ is small $\tan\gamma\approx\gamma$ and the equation becomes:
$$AB \approx L\gamma$$