Moment of Inertia (Thin Rod)

📊 intermediate

$$I = \frac{1}{12}ML^2$$

The rotational inertia of a uniform thin rod rotating about an axis through its center perpendicular to its length.

Variables & Units

$L$

Total length of rod

Unit: Meter ($m$)

Key Information

📐 Derived From

Integration of $x^2 dm$ along the length of the rod.

💡 Example

Calculating rotational inertia of a baton.

🔧 Applications

Structural mechanics and pendulum design.

⚠️ Constraints

Uniform linear density; axis through center.

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