PH8151EPUnit1

22 CHAPTER 1. PROPERTIES OF MATTER

1.7.1 Torsion Pendulum - Determination of Rigidity Modulus

of Suspension Wire

Consider the suspension fibre of a torsion pendulum as a thin cylinder of lengthland
radiusrfixed at the top end and twisted at the free end by an angle◊as shown in Figure
1.21. Due to the elasticity of the wire, an internal restoring force is developed in the wire

P x

Q

A

B

C

φ

θ

dx

r

l

Fixed End

Free End

(twisted)

Figure 1.21: Couple per unit twist

and it is said to be in torsion.
The Rigidity Modulus of the wire (n) = (shear stress) / (shear strain).

Hence, shear stress,=n◊(shear strain) (1.7)

We first consider an imaginary cylindrical shell of outer radiusxand thickness dxas
shown in Figure1.21and calculate the shear stress at this shell. A vertical line AB drawn
on the shell get shifted to the position AC due to the torsional deformation, resulting in
an angle of twist\BQC=◊ and an angle of shear\BAC=„.Itcanbeseenfrom
Figure1.21thatBC=l„=x◊. Therefore,

shear strain,„=

x◊

l

(1.8)

Therefore from equations (1.7) and (1.8), at the imaginary shell,

shear stress,=n◊

x◊

l

(1.9)

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