# Torsion of a Cylinder Physics | Definition, Formula, Units – Elasticity

Torsion of a Cylinder Definition:
1. Torsion is the twisting of an object due to an applied torque. In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.

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## Torsion of a Cylinder | Definition, Formula, Units – Elasticity

2. If the upper end of a cylinder is clamped and a torque is applied at the lower end the cylinder get twisted by angle θ, then Couple per unit twist,

C = $$\frac{\pi \eta r^{4}}{2 l}$$

where,
η = Modulus of rigidity of the material of cylinder,
r = Radius of cylinder and
l = length of cylinder.

Work done in twisting the cylinder through an angle θ

W = $$\frac{1}{2} C \theta^{2}$$

Relation between angle of twist (θ) and angle of shear (Φ)
rθ = lΦ
or
Φ = $$\frac{r}{l} \theta$$

Elasticity:
Elasticity defines a property of an object that has the ability to regain its original shape after being stretched or compressed. Learn about the deforming force applied on an elastic object and how the stress and strain works on an object. What is a Hooke’s law and how it is applicable for the concept of elasticity.