Rigidity or shear modulus
The stress = tangential force
(F)/ area over which applied (A)
The strain = angle of shear =
x/y - for small angles.
Therefore:
Rigidity or shear modulus (G) = [F/A]/[θ]
For a wire the restoring
torque (T) when twisted through an angle θ
is
Restoring torque (T) = cθ
where c is a
constant.
This
means that a wire will twist by a large amount for a given torque if its
modulus of rigidity is small. The ability to resist or allow twisting is
of vital importance in the design of buildings and in the materials used
for drive shafts in engines and suspensions in meters. Clearly a drive
shaft with low rigidity would be useless, as would a meter suspension
with a very high rigidity.
If a spiral spring is stretched all
parts of the spring will become twisted. The extension of the spring
therefore depends on both its modulus of rigidity and size.
Student investigation
If you have ever watched a tree bending in a gale you will appreciate that plants of all types are subject to many and varied forces.
Investigate the bending of specimens such as grass and plant stems. How do their elastic properties compare with similarly sized specimens of nylon or copper?
A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB
