A $1\mathrm{.}5-$in$.-$diameter steel shaft of length $4$ ft will be used to transmit $64\mathrm{.}5$ hp between a motor and a pump. Knowing that $G=11\mathrm{.}2{10}^6$

psi, determine the lowest speed of rotation at which the stress does not exceed $8500$ psi and the angle of twist does not exceed $2.$

The lowest speed of rotation at which the stress does not exceed $8500$ psi and the angle of twist does not exceed $2$ is