Angle of twist:
When a twisting couple is applied to the lower face of a cylinder, clamped at the upper end, in a direction perpendicular to the length of the cylinder, the radius of the lower end twisted through an angle \( \theta \), which is known as the angle of twist.
Since the twist neither produces a change in the radius of the cylinder nor a change in the length of the cylinder, this is an example of pure shear.
Angle of shear:
When a twisting couple is applied to a cylinder, a line on the rim of that cylinder parallel to its axis is displaced through an angle \( \phi \), which is known as the angle of shear.
In the Fig.1, angle of twist is represented by \( \angle{POQ}=\theta \) and the angle of shear is represented by \( \angle{PMQ}=\phi \).