The Flywheel Energy Calculator determines how much rotational energy is stored in a spinning flywheel. This type of calculator is especially useful in mechanical and energy storage applications, such as in vehicles, industrial equipment, and renewable energy systems. By using a few basic physical properties—mass, radius, and rotational speed—it helps engineers, technicians, and students quantify the energy that a flywheel system can store and deliver.
This tool belongs to the category of Mechanical Energy and Rotational Dynamics Calculators.
formula of Flywheel Energy Calculator
Energy (E) = (1/2) × I × ω²
Where:
E = Energy stored (in joules, J)
I = Moment of inertia of the flywheel (in kg·m²)
ω = Angular velocity (in radians per second, rad/s)
Moment of Inertia (I) for Solid Disk Flywheel
I = (1/2) × m × r²
Where:
m = Mass of the flywheel (kg)
r = Radius of the flywheel (m)
Angular Velocity (ω) from RPM
ω = (2 × π × RPM) / 60
Where:
RPM = Rotational speed in revolutions per minute
This approach combines rotational mechanics with real-world measurements like RPM and mass to yield a precise energy estimate.
Reference Table for Common Flywheel Calculations
| Term | Description |
|---|---|
| RPM | Rotations per minute |
| π | Approximately 3.1416 |
| ω (rad/s) | Angular velocity |
| Moment of Inertia (I) | Depends on mass and radius |
| Energy (J) | Energy stored in the flywheel |
| 1 kWh | 3.6 million joules (conversion reference) |
This table can assist users in quickly recalling or converting units related to flywheel dynamics.
Example of Flywheel Energy Calculator
Scenario:
A flywheel has a mass of 100 kg and a radius of 0.5 meters. It spins at 1500 RPM.
Step 1: Calculate Moment of Inertia (I)
I = (1/2) × m × r²
I = (1/2) × 100 × 0.5² = 12.5 kg·m²
Step 2: Convert RPM to ω
ω = (2 × π × RPM) / 60
ω = (2 × 3.1416 × 1500) / 60 ≈ 157.08 rad/s
Step 3: Calculate Energy
E = (1/2) × I × ω²
E = (1/2) × 12.5 × (157.08)² ≈ 154,158 joules
So, the flywheel stores approximately 154,158 joules of energy.
Most Common FAQs
A flywheel stores kinetic energy in the form of rotational motion. When needed, this energy can be converted back into mechanical or electrical energy.
Yes. Energy storage increases with higher mass, larger radius, or faster rotational speed. Since energy is proportional to the square of the speed, doubling RPM significantly boosts energy.
Flywheels are commonly used in hybrid vehicles, uninterruptible power supplies, industrial machinery, and renewable energy systems to manage energy flow and improve efficiency.