Find rotational torque from measured angular acceleration. Choose inertia by shape or enter a value. Export calculations fast, and compare multiple scenarios with ease.
| Scenario | Method | Inputs | Output |
|---|---|---|---|
| Flywheel torque | Direct inertia | I=0.35 kg·m², α=8 rad/s² | τ=2.80 N·m |
| Rod about center | Shape-based inertia | m=2 kg, L=0.9 m, α=5 rad/s² | τ≈0.675 N·m |
| Find angular acceleration | Direct inertia | τ=10 N·m, I=0.5 kg·m² | α=20 rad/s² |
The calculator is based on Newton’s second law for rotation:
Shape-based inertia uses standard forms such as I=½mr² (disk), I=mr² (thin ring), and I=(1/12)mL² (rod about center).
Rotational motion links cause and response: a net torque produces angular acceleration. This calculator connects measured α to torque through the moment of inertia I, which depends on mass distribution. Use it for flywheels, drums, spindles, and lab rigs when geometry or inertia is known. It also helps back-calculate inertia from known torque and acceleration during commissioning tests, maintenance checks, and classroom demonstrations of dynamics in practice.
With constant inertia, τ = I·α is linear: doubling α doubles τ. Example: I = 0.35 kg·m² and α = 8 rad/s² gives τ = 2.8 N·m; α = 16 rad/s² gives 5.6 N·m. Linearity helps compare designs quickly.
Small rotors can be 10⁻⁴ to 10⁻² kg·m², mid-sized flywheels often 0.05 to 1 kg·m², and heavy drums several kg·m² or more. If torque looks unrealistic, recheck radius units because inertia usually scales with r².
Common checks: 1 lbf·ft ≈ 1.3558 N·m, and 1 rad/s² ≈ 57.2958 deg/s². If α is entered in deg/s², it must be converted to rad/s² before applying τ = I·α. Consistent units prevent huge errors.
Standard forms include I = ½mr² (solid disk), I = mr² (thin ring), and I = (1/12)mL² (rod about center). These assume uniform density and the stated axis. Moving mass outward increases I strongly, raising the torque needed for the same α.
From encoder data, compute α from the slope of ω versus time over a steady interval. Averaging over 0.2–1.0 s reduces noise. Run three trials and compare results; consistent torque values usually indicate a stable measurement window.
A quick estimate is Δτ/τ ≈ ΔI/I + Δα/α. For inertia based on r², a 2% radius error can contribute about 4% inertia error. Measure dimensions carefully, confirm the rotation axis, and for hollow parts, keep inner and outer radii consistent.
It solves τ, α, or I using τ = I·α. You can enter inertia directly or estimate it from common shapes and mass, then export results as CSV or PDF.
Use it when you know the object’s mass and dimensions but not its inertia. It works best for uniform shapes like disks, rings, rods, spheres, and plates with standard rotation axes.
The rotational law uses SI radians. If your data is in deg/s², it must be converted. This calculator converts deg/s² to rad/s² automatically before computing torque.
Verify inertia units and radius/length units first. Inertia often depends on r², so a unit mix-up (cm vs m) can inflate torque by 10,000×. Also confirm the chosen shape formula matches the axis.
It gives required torque for a desired acceleration, but real motors need extra torque for friction, windage, and load changes. Add a safety margin and include drivetrain efficiency when selecting a motor.
Yes. Moving mass outward increases inertia dramatically. A thin ring has greater inertia than a solid disk with the same mass and radius, so it needs more torque to achieve the same angular acceleration.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.