# Real formula for gamma(deformation) in torsion of a rod?

 P: 1 Okay, so I'm studying for a Mechanics of Materials final at the moment, and I am reviewing the chapter on torsion. I was reading through the given formulae, and I stumbled across one that I could not fully visualize (or simplify): the formula for gamma. Based on my understanding and from what I know from before, shouldn't the formula: $\gamma$=$\rho$$\phi$ / L (for the deformation of a rod under torsion) actualy be sin($\gamma$) = $\rho$$\phi$/L ? Correct me if I am wrong, but aren't we considering rho*phi to be the arc length of the end deformation, and considering that arc length to be the opposite side of the angle gamma in the pseudo-right triangle formed when the rod deforms? I have come with two possible reasons for my confusion 1) The book is not using the sine function because the angle is very very small. 2) I am failing to realize what kind of geometric scenario is occuring between the angle gamma and the arc length rho*phi. Please get back to me with a response as soon as possible so I can move on from being miserably confused! :P
 P: 343 The answer is in your first possible reason. This is a small angle approximation, and actually, it is a very good approximation, provided the length L is several times rho.
 P: 34 Yes, nice observation, but as OldEngr63 pointed out, this is for small rotations. So sin(gamma) would approximately be gamma.

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