Torsion pendulum - Rigidity modulus (without masses)

                                                                      

    The Torsion Pendulum experiment for measuring the Rigidity Modulus is an important part of the first-year B.Sc. Physics practicals in the TANSCHE curriculum. This experiment allows students to dive into the idea of rigidity modulus, which is also called shear modulus. It’s a key characteristic of materials that shows how well they can withstand deformation when subjected to shear stress. By utilizing a torsion pendulum, students can find the rigidity modulus of a specific wire or material through careful measurements and calculations.

    In this article, we will walk you through the experimental process, offering a clear, step-by-step guide on how to set up the torsion pendulum, perform the experiment, and compute the rigidity modulus. Grasping this experiment is vital for understanding the mechanical properties of materials, which is a fundamental part of both physics and material science.

Torsion pendulum - 

Rigidity modulus (without masses)

Aim:

To determine the rigidity modulus of the material of a wire by the method of torsional oscillations of the torsion pendulum.

Apparatus required:

Torsion pendulum (circular disc), stop clock, meter scale, screw gauge, thread etc

Formula:

Rigidity modulus of the wire is,

Here,

G is the rigidity modulus of the material of a wire N/m2
a is the radius of the wire m
T is the period of oscillation s
L is the length of the wire m
I is the moment of inertia of the circular disc kg.m2
    
M is the mass of the circular disc kg
R is the radius of the circular disc m

Procedure:

The wire's length between the fixed end and the chuck in the circular disc is adjusted to a length L. A reference line is marked on the disc. The disc is then gently twisted in a horizontal direction and released. It begins to perform torsional oscillations. 

The time taken for 10 oscillations is recorded. This process is repeated for different L values to find the average time for 10 oscillations. From this, the period T is calculated. The radius (a) of the wire is measured with a screw gauge.

With the help of a thread the circumference of a disc is measured and then radius is found out. Then the mass of the disc is measured. From these values the moment of inertia can be calculated.

Tabular Column 1: To find the the L/T2

S.No	Length L m	Time for 10 oscillations s			Time period s	L/T2 m/s2
		Trial 1	Trial 2	Mean

Tabular Column 2: To find the thickness of the beam using screw gauge

    The procedure of using Screw gauge and its table can be found here.

    From the average diameter (d) of the wire can be calculated. From this radius (a) can be found.

Result: 

    The rigidity modulus of the material of the wire using torsional pendulum is found to be as, G = ______ N/m2