# Experimental Determination of Moment of Inertia on Incline
> Learn how to calculate and compare the Moment of Inertia for cylinders and spheres using an inclined plane experiment and energy conservation formulas.

Tags: physics-experiment, moment-of-inertia, rotational-dynamics, classical-mechanics, inclined-plane, science-lab, conservation-of-energy
## Determination of Moment of Inertia
* Experimental analysis of solid cylinders, hollow cylinders, and solid spheres.

## Objective
* To experimentally determine the Moment of Inertia (I) of various rigid bodies and verify theoretical predictions through kinematics on an inclined plane.

## Apparatus Required
* Adjustable inclined plane, solid/hollow cylinders, solid sphere, Vernier calipers, electronic balance, and digital timing sensors.

## Theory & Formulas
* **Energy Equation:** mgh = ½mv² + ½Iω²
* **Solid Cylinder:** I = ½ MR²
* **Hollow Cylinder:** I ≈ MR²
* **Solid Sphere:** I = ⅖ MR²

## Dynamics on an Incline
* Analysis of forces: gravity components (mg sin θ, mg cos θ), normal force (N), and friction (f) which provides necessary torque for rolling.

## Procedure & Calculation
* Measure mass and radius of test objects.
* Record rollout time (t) over distance (s) from rest.
* Calculate linear acceleration: a = 2s / t²
* Determine experimental inertia: a = g sin(θ) / (1 + I/MR²)

## Results Summary
* Observed values for Mass=1kg, Radius=0.1m:
    * **Solid Sphere:** Theoretical I = 0.004, Experimental I = 0.0042
    * **Solid Cylinder:** Theoretical I = 0.005, Experimental I = 0.0053
    * **Hollow Cylinder:** Theoretical I = 0.01, Experimental I = 0.0105

## Discussion & Conclusion
* The sphere reached the bottom fastest due to lower inertia.
* Mass distribution significantly impacts rotational resistance.
* Error analysis attributed slight discrepancies to micro-slippage and air resistance.
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