The Flywheel Momentum Calculator estimates the angular momentum stored in a rotating flywheel. This measurement helps engineers and designers understand how much rotational motion the system contains and how resistant it is to changes in speed. Flywheel momentum plays a critical role in mechanical energy systems, energy storage applications, and industrial machinery that rely on consistent rotational force.
This calculator falls under the category of Rotational Mechanics and Dynamics Calculators. It is especially valuable in industries like automotive engineering, power systems, and renewable energy storage where efficient energy transfer and rotational inertia matter.
formula of Flywheel Momentum Calculator
Angular Momentum (L) = I × ω
Where:
L = Angular momentum (in kg·m²/s)
I = Moment of inertia of the flywheel (in kg·m²)
ω = Angular velocity (in radians per second)
Moment of Inertia for a Solid Disk
I = (1/2) × m × r²
Where:
m = Mass of the flywheel (in kg)
r = Radius of the flywheel (in meters)
Angular Velocity from RPM
ω = (2 × π × RPM) / 60
Where:
RPM = Rotational speed in revolutions per minute
Combined Formula (if RPM, mass, and radius are known)
L = (1/2) × m × r² × [(2 × π × RPM) / 60]
This combined version allows you to calculate momentum directly from practical input values like flywheel mass, radius, and rotation speed.
Reference Table for Quick Insights
| Parameter | Description |
|---|---|
| Angular Momentum (L) | Rotational momentum stored in the flywheel |
| Moment of Inertia (I) | Resistance to angular acceleration |
| RPM | Speed in revolutions per minute |
| Angular Velocity (ω) | Speed in radians per second |
| 1 radian | Approximately 57.3 degrees |
| π | Approximately 3.1416 |
| 1 kg·m²/s | SI unit for angular momentum |
This table helps users recognize essential concepts and units used in flywheel dynamics.
Example of Flywheel Momentum Calculator
Scenario:
A flywheel has a mass of 50 kg and a radius of 0.3 meters. It spins at 1200 RPM.
Step 1: Moment of Inertia
I = (1/2) × m × r²
I = (1/2) × 50 × (0.3)² = (1/2) × 50 × 0.09 = 2.25 kg·m²
Step 2: Convert RPM to Angular Velocity
ω = (2 × π × 1200) / 60 = (2 × 3.1416 × 1200) / 60 ≈ 125.66 rad/s
Step 3: Calculate Angular Momentum
L = I × ω = 2.25 × 125.66 ≈ 282.74 kg·m²/s
So, the angular momentum of the flywheel is approximately 282.74 kg·m²/s.
Most Common FAQs
Flywheel angular momentum is used to store and transfer rotational energy. It helps maintain smooth mechanical operation, especially in systems that experience variable loads or interruptions in power.
Yes. Angular momentum increases directly with angular velocity (RPM). A faster-spinning flywheel stores more momentum, making it more effective for energy buffering.
Yes. Both mass and radius impact the moment of inertia. A larger or heavier flywheel has more inertia, which increases the total angular momentum when spinning.