The Flywheel Torque Calculator determines the torque applied to or generated by a rotating flywheel based on its moment of inertia and angular acceleration. Torque is essential in mechanical systems because it directly influences rotational motion and energy transfer. This tool is commonly used in engineering applications involving energy storage, machinery, automotive systems, and industrial design.
This calculator falls under the Rotational Mechanics Calculator category and supports design, analysis, and diagnostics of rotating mechanical systems with high reliability.
formula of Flywheel Torque Calculator
Torque (τ) = I × α
Where:
τ = Torque (in newton-meters, N·m)
I = Moment of inertia of the flywheel (in kg·m²)
α = Angular acceleration (in radians per second squared, rad/s²)
1. Moment of Inertia for a Solid Disk Flywheel
I = (1/2) × m × r²
Where:
m = Mass of the flywheel (in kg)
r = Radius of the flywheel (in meters)
2. Angular Acceleration
α = (ω₂ − ω₁) / Δt
Where:
ω₁ = Initial angular velocity (in rad/s)
ω₂ = Final angular velocity (in rad/s)
Δt = Time interval for the change in speed (in seconds)
To convert RPM to rad/s:
ω = (2 × π × RPM) / 60
Using these formulas together, you can compute torque based on the flywheel’s physical characteristics and how quickly its rotational speed changes.
Common Reference Table
| Term | Description |
|---|---|
| Torque (τ) | Rotational force produced or resisted |
| Moment of Inertia (I) | Resistance of flywheel to angular acceleration |
| Angular Acceleration (α) | Rate of change of angular velocity |
| RPM to rad/s conversion | ω = (2 × π × RPM) / 60 |
| 1 newton-meter (N·m) | Torque unit, equivalent to force × distance |
| 1 kg·m² | Standard unit of moment of inertia |
| π | Approx. 3.1416 |
This table helps clarify key concepts and units, making it easier to use the calculator accurately.
Example of Flywheel Torque Calculator
Scenario:
A flywheel with a mass of 20 kg and a radius of 0.3 meters is accelerated from 600 RPM to 1200 RPM over 10 seconds. What is the torque applied?
Step 1: Calculate Moment of Inertia (I)
I = (1/2) × m × r² = (1/2) × 20 × 0.3² = 0.5 × 20 × 0.09 = 0.9 kg·m²
Step 2: Convert RPM to rad/s
ω₁ = (2 × π × 600) / 60 ≈ 62.83 rad/s
ω₂ = (2 × π × 1200) / 60 ≈ 125.66 rad/s
Step 3: Calculate Angular Acceleration (α)
α = (125.66 − 62.83) / 10 ≈ 6.283 rad/s²
Step 4: Calculate Torque (τ)
τ = I × α = 0.9 × 6.283 ≈ 5.65 N·m
Answer:
The torque applied is approximately 5.65 newton-meters.
Most Common FAQs
Flywheel torque calculations help engineers determine the required force to accelerate or decelerate rotating components. It is critical for performance tuning, energy efficiency, and system safety.
Yes, but you must use the correct formula for moment of inertia based on the flywheel’s shape. The solid disk formula is just the most common. Hollow cylinders or complex geometries need different equations.
They are very accurate when π is approximated to at least four decimal places (3.1416). This level of accuracy is sufficient for most engineering and educational purposes.