Moment of Inertia (Point Mass)

📊 beginner

$$I = mr^2$$

Rotational inertia of a point mass about an axis.

Variables & Units

$I$

Moment of inertia

Unit: $\text{kg·m}^2$

$m$

Mass

Unit: $\text{kg}$

$r$

Perpendicular distance from axis

Unit: $\text{m}$

Key Information

📐 Derived From

$I = \sum m_i r_i^2$ for discrete masses.

💡 Example

A $0.5\,\text{kg}$ mass at $0.2\,\text{m}$ from axis: $I = 0.5 \times (0.2)^2 = 0.02\,\text{kg·m}^2$.

🔧 Applications

Flywheels, pendulums, robotics.

⚠️ Constraints

Rigid body, fixed axis.

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