The shear stress $\mathrm{\tau }$ in a shaft is related to the torque by the torsion formula $\mathrm{\tau }=\mathrm{Tc}/\mathrm{J}$. The angle of twist $\mathrm{\varphi }$ is related to the torque by the formula $\mathrm{\varphi }=\mathrm{TL}/\mathrm{JG}$. The torque that can be applied to the shaft must satisfy two conditions:

• the shear stresses must be kept to an acceptably low value and

• the angle of twist must be kept below a specified limit.

Once this limiting torque is obtained, the power-torque formula can be used to find the power transmitted by the shaft at the limiting torque and the specified rotation speed.