Measuring Modulus of Rigidity Using Maxwell’s Needle

Experiment No. 1: Modulus of Rigidity

Using Maxwell’s Needle / Barton’s Apparatus

Objective

To determine the Modulus of Rigidity of a given wire by Static and Dynamic methods using Maxwell’s needle or Barton’s apparatus.

Apparatus Required

Maxwell’s Needle

Torsion Wire

Stopwatch & Meter Scale

Stand & Clamps

Theoretical Background

Modulus of Rigidity (η) is defined as the ratio of shear stress to shear strain within the elastic limit.

The Formula

η = (8π² I L) / (T² r⁴)

I = Moment of Inertia

L = Length of the wire

T = Time period of oscillation

r = Radius of the wire

Experimental Diagram

Procedure Steps

1. Suspend the Maxwell's needle using the torsion wire.

2. Gently rotate the needle to allow torsional oscillations.

3. Measure the time period (T) for a fixed number of oscillations using a stopwatch.

4. Calculate the Modulus of Rigidity using the formula.

Key Concepts: Torsional Oscillation

When the needle acts as a torsional pendulum, the restoring torque is directly proportional to the angular displacement. The time signal period depends on the inertia of the system and the stiffness of the wire.

Result & Discussion

The time period of oscillation was observed to depend significantly on the distribution of mass in the system. As the mass moves further from the axis of rotation, the Moment of Inertia (I) increases, thereby increasing the Time period (T).

Conclusion

The Modulus of Rigidity of the given wire material has been successfully determined using the dynamic method with Maxwell's Needle. The experiment confirms the relationship between torsional stiffness and the wire's physical dimensions.