Solution
= Solution
The <torque> rises linearly with elastic twist, so the stored <elastic energy> is the work integral
$$
U=\int_0^\phi\frac{GJ_p}{L}\phi'\,d\phi'
=\frac12C\phi.
$$
Using the transmitted torque and end twist,
$$
\boxed{U\simeq\frac12(133.3)(1.243\times10^{-3})\ \mathrm J
=8.29\times10^{-2}\ \mathrm J.}
$$
This is energy associated with deformation, distinct from the much larger kinetic energy of the whole spinning shaft.