Aim:

To determine the rigidity modulus of the suspension wire using torsion pendulum.

Apparatus:

The given torsion pendulum, two identical cyllindrical masses, stop watch, metre scale, etc.

Theory:

  What is Torsional Oscillation?

A body suspended by a thread or wire which twists first in one direction and then in the reverse direction, in the horizontal plane is called a torsional pendulum.The first torsion pendulum was developed by Robert Leslie in 1793.

A simple schematic representation of a torsion pendulum is given below,

The period of oscillation of torsion pendulum is given as,

Where   I=moment of inertia of the suspended body; C=couple/unit twist 

But we have an expression for  couple per unit twist C as,

Where   l =length of the suspension wire; r=radius of the wire; n=rigidity modulus of  the suspension wire

Substituting (2) in (1) and squaring,we get an expression for rigidity modulus for the suspension wire as,

We can use the above formula directly if we calculate the moment of inertia of the disc,I as (1/2)MR².

Now,let I₀  be the moment of inertia of the disc alone and I₁ & I₂ be the moment of inertia of the disc with identical masses at distances d₁&d₂ respectively.If  I^₁ is the moment of inertia of each identical mass about the vertical axis passing through its centre of gravity, then

But from equation (1) ,

Where T₀,T₁,T₂ are the periods of torsional oscillation without identical mass,with identical pass at position d₁,d₂ respectively.

Dividing equation (6) by (9) and using (5),

Therefore,The moment of inertia of the disc,

Now substituting equation (2) and (5) in (9),we get the expression for rigidity modulus 'n' as,

 Applications of Torsional Pendulum:

1.The working of  " Torsion pendulum clocks " ( shortly torsion clocks or pendulum clocks), is based on torsional oscillation.

2.The freely decaying oscillation of  Torsion pendulum in medium(like polymers),helps to determine their characteristic properties.

3.New researches, promising the determination of frictional forces between solid surfaces and flowing liquid environments using forced torsion pendulums.