Torsion pendulum - Rigidity modulus (with 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 (with 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), two identical weights, 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
M is the mass of the circular disc kg
M is the mass of each of two symmetrical weights kg
T0 is the period of oscillation without weights s
T1 is the period of oscillation with weights at distance d1 s
T2 is the period of oscillation with weights at distance d2 s
d1 is the distance between the weights when they are closest to each other m
d2 is the distance between the weights when they are far from each other m
L is the length of the wire m
I is the moment of inertia of the circular disc kg.m2

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 to find the average time for 10 oscillations. From this, the period T0 is calculated. 

        Two identical masses are positioned evenly on both sides of the suspension wire, each located a distance d1 (close to the wire) from the center (where d1 is the space between the center of the disc and the center of each mass). The period T1 is measured.

        After that, the masses are kept at the distance d2 (far from the wire) from the center, and the period T2 is measured again. The time periods are measured for various lengths. The radius (a) of the wire is measured with a screw gauge. 

d1 = _____ cm d2 = _____ cm

Tabular Column 1: To find the the time period

S.No	Length L m	Position of weights	Time for 10 oscillations s			Time period s
			Trial 1	Trial 2	Mean
		without
		at d1
		at d2
		without
		at d1
		at d2

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

Result: 

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