Work-Energy Theorem (Rotational)

📊 advanced

$$W = \Delta K_{\text{rot}} = \frac{1}{2} I \omega_f^2 - \frac{1}{2} I \omega_i^2$$

The net work done by all torques acting on a rigid body is equal to the change in its rotational kinetic energy.

Variables & Units

$W$

Rotational work

Unit: Joule ($J$)

$I$

Moment of inertia

Unit: $kg \cdot m^2$

$\omega$

Angular velocity

Unit: rad/s

Key Information

📐 Derived From

Integration of torque with respect to angular displacement.

💡 Example

Work done to spin up a flywheel.

🔧 Applications

Mechanical energy storage and gyroscope analysis.

⚠️ Constraints

Rigid body rotating about a fixed axis.

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