ASTM$-$A$709$ Grade $690$ steel of same diameter is to be used for shafts AB and CD$.$ It is required that that the angular deflection $\backslash (\backslash$boldsymbol$\{\backslash$phi$\}\_\{\backslash$mathrm$\{$D$\}\}\backslash )$ at the end of shaft CD not exceed $\backslash (\backslash$mathbf$\{2.0\}\{\}^\{\backslash$circ$\}\backslash ).$

a$)$ Determine the required diameter of the shafts, using a factor of safety $\backslash (\backslash$mathbf$\{$n $=2.5\}\backslash )$

b$)$ If A should be rotating at $1450$ rpm $,$ what power would be carried through the system?