A motor driving a solid circular steel shaft with diameter $\backslash ($ d$=4\backslash$mathrm$\{$~cm$\}\backslash )$ rotates at $150$ rpm to transmit power to a gear at $\backslash ($ B $\backslash ).$ The allowable shear stress in the steel is $45$ MPa and the allowable angle of twist is $\backslash (1^\{\backslash$circ$\}\backslash ).$ Calculate the maximum power the shaft can transmit so that both the shear stress and angle of twist in the shaft do not exceed the allowable limits$.$ Consider the shear modulus of elasticity of the shaft as $75$ GPa $,$ and that the length of the shaft between the motor and the gear $\backslash ($ B $\backslash )$ is $0\mathrm{.}5$ m $.$