Torque T is applied on a shaft of length L at either ends in opposite directions. The radial and longitudinal lines are shown on the shaft. The deformation of the shaft is shown with a counterclockwise segment of angle phi, angle of twist.

We can combine a couple of earlier expressions to produce an alternative formula for the angle of twist. Recall:

γmax=L

Using Hooke's law, an expression for τmax can be obtained by multiplying by G:

τmax=GcϕL

Setting this equal to the torsion formula, we can solve for the angle of twist ϕ:

ϕ=TLJG