Answer by sc_ for Identify $f$, $f'$, $u$ and $u'$ in an equation to use...
$u$ and $f$ are as follows:\begin{align}u(R_1) &= \frac{\pi}{2}(R_{2}^{4}-R_{1}^{4})\\&= J\\f(J) &= \frac{1}{J}\\f'(J) &= -\frac{1}{J^2}\\u'(R_1) &=...
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A hollow tube of length $L$, inner radius $R_{1}$ and outer radius $R_{2}$ is twisted by an angle $\alpha$ by applying a moment $M$. The angle $\alpha$ is a function of the inner radius...
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