🔄 Rotational Dynamics & Mechanics
Mass Moment of Inertia Converter
Convert rotational inertia ($I = \int r^2 dm$) across SI ($\text{kg}\cdot\text{m}^2$), imperial ($\text{lb}\cdot\text{ft}^2, \text{slug}\cdot\text{ft}^2$), and CGS ($\text{g}\cdot\text{cm}^2$) systems.
🚲 Bicycle Wheel (0.14 kg·m²)
🚗 Engine Flywheel (0.15 kg·m²)
⚡ Motor Rotor (0.025 kg·m²)
🌬️ Wind Turbine (50k kg·m²)
Input Rotational Inertia
Standard Imperial (lb·ft²)
23.73 lb·ft²
kg·m²
1.000 kg·m²
slug·ft²
0.7376
g·cm²
1.00 × 10⁷
💡 Rotational Dynamics Equivalence:
$$1\text{ kg}\cdot\text{m}^2 = 23.73\text{ lb}\cdot\text{ft}^2 = 0.7376\text{ slug}\cdot\text{ft}^2 = 10^7\text{ g}\cdot\text{cm}^2$$
Mass Moment of Inertia Principles
Mass moment of inertia ($I$) measures an object's resistance to angular acceleration about an axis of rotation:
- Rotational Kinetic Energy: $$E_k = \frac{1}{2} I \omega^2$$
- Angular Momentum: $$L = I \omega$$
- Torque & Angular Acceleration: $$\tau = I \alpha$$
- Conversion Factors: $1\text{ kg}\cdot\text{m}^2 = 23.73036\text{ lb}\cdot\text{ft}^2 = 0.737562\text{ slug}\cdot\text{ft}^2 = 3,417.17\text{ lb}\cdot\text{in}^2$.