Moment of Inertia (Solid Sphere)

📊 advanced

$$I = \frac{2}{5}MR^2$$

The rotational equivalent of mass for a uniform solid sphere rotating about its diameter.

Variables & Units

$M$

Mass

Unit: Kilogram ($kg$)

$R$

Radius

Unit: Meter ($m$)

Key Information

📐 Derived From

Integration of $\int r^2 dm$ over the sphere's volume.

💡 Example

Calculating MI of a bowling ball.

🔧 Applications

Stability of planets and ball bearing design.

⚠️ Constraints

Uniform density; axis through center.

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