# Measuring Modulus of Rigidity Using Maxwell’s Needle
> Learn how to determine the Modulus of Rigidity (η) of a wire using Maxwell’s needle or Barton’s apparatus with static and dynamic methods.

Tags: physics-experiment, modulus-of-rigidity, maxwells-needle, torsional-oscillation, material-science, engineering-physics, lab-report
## Experiment No. 1: Modulus of Rigidity
* **Objective:** Determine the Modulus of Rigidity of a wire using static and dynamic methods via 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):** 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

## Procedure Steps
1. Suspend the Maxwell's needle using the torsion wire.
2. Gently rotate the needle to initiate 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
* The needle acts as a torsional pendulum where restoring torque is proportional to angular displacement.
* The period of signal depends on the system's inertia and wire stiffness.

## Result & Discussion
* The time period (T) depends on mass distribution. Moving mass further from the rotation axis increases the Moment of Inertia (I), which increases the Time period (T).

## Conclusion
* The experiment successfully determined the Modulus of Rigidity of the wire material using the dynamic method, confirming the relationship between torsional stiffness and physical dimensions.
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