A solid circular rod is used to transmit power from a motor to a machine. The diameter of the rod is D$=2\mathrm{.}5$ inin and the machine operates at $=130$ rpmrpm $.$ If the allowable shear stress in the shaft is $11\mathrm{.}8$ ksiksi $,$ what is the maximum power transmissible to the machine?

Express your answer with appropriate units to three significant figures. A solid circular shaft is required to transmit P$=48$ kWkW from a motor to a machine. The maximum allowable stress in the shaft is allow$$allow $=79$ MPaMPa $.$ If the machine runs at $=19$ rad$/$srad$/$s $,$ what is the minimum diameter for the shaft?

Express your answer in cm to three significant figures.