(Solved): [20 points] A solid circular bar is fixed to a wall at x=0 and is loaded by a distributed torque th ...

[20 points] A solid circular bar is fixed to a wall at $x=0$ and is loaded by a distributed torque that linearly increases in intensity from 0 at $x=0$ (point $A$ ) up to a maximum value at $x=L$ (point $B$ ) of $t_0=500[\mathrm{N}?\mathrm{m}/\mathrm{m}]$. The bar has a length $L=2[\mathrm{m}]$, has a diameter of $10[\mathrm{mm}]$, and is made of steel $(G=75[\mathrm{GPa}])$ Determine the reaction torque at $A$, and the angle of twist at $B$. Hint: The distributed torque $t(x)$ has units of torque per unit length (i.e. $(\mathrm{N}?\mathrm{m})/\mathrm{m})$. As an example of how to think about distributed torques, consider that you would calculate the total torque on the bar through a simple integration: $T_{\text{tot }}={?}_0^{L}t(x)dx$ and also consider Eq. 10.17. NOTE: You may assume the steel is a HILE material (feel free to comment on the validity of this assumption in your Reflect \& Think step). Ans. $T_A=500[\mathrm{N}?\mathrm{m}],?=1.132[\mathrm{rad}]$.