Let's return to our geometry from problem $2.$ To repeat: The system below is hollow from $B$ to $C$ with outer$/$inner diameters of $4$ and $2$ inches. But now we add that the length is $20$ inches with $G=18,000$ ksi. The section from $C$ to $D$ is solid with a diameter of $2\mathrm{.}5$ inches with a length of $8$ inches and $G=10,000$ ksi. Find the rotation of $C$ and $D($say "double arrow to the left$/$right$")$ to indicate direction. Answers: ${}_C=0\mathrm{.}000236$ rad double arrow left, ${}_D=0\mathrm{.}00039$rad double arrow right.