Measure tangential acceleration from angular change and radius. Switch units, compare cases, and inspect trends. Export results, study formulas, and visualize motion behavior clearly.
If you only need angular acceleration converted into linear acceleration, the main relation is aₜ = α × r. The added velocity-based outputs give a fuller rotational motion analysis.
| Case | α (rad/s²) | r (m) | ω (rad/s) | aₜ (m/s²) | a_c (m/s²) | Total (m/s²) |
|---|---|---|---|---|---|---|
| Lab disk | 8.00 | 0.15 | 12.00 | 1.20 | 21.60 | 21.63 |
| Wheel rim | 15.00 | 0.30 | 20.00 | 4.50 | 120.00 | 120.08 |
| Turntable edge | 5.50 | 0.18 | 6.00 | 0.99 | 6.48 | 6.56 |
| Motor shaft | 22.00 | 0.05 | 40.00 | 1.10 | 80.00 | 80.01 |
It converts angular acceleration and radius into tangential linear acceleration. When angular velocity is also supplied, it adds linear velocity, centripetal acceleration, and total acceleration for a fuller rotational motion picture.
The key relation is aₜ = α × r. Angular acceleration must be in rad/s² and radius in meters to produce tangential acceleration in m/s² before any display conversion.
For the same angular acceleration, a point farther from the axis travels a longer arc in the same time. That larger path change creates a larger tangential linear acceleration.
Angular velocity is not needed for tangential acceleration from α and r. It becomes useful when you want centripetal acceleration, total acceleration, and linear speed at the same radius.
A negative angular acceleration produces a negative tangential acceleration sign, indicating direction opposite the chosen positive rotation. The total acceleration magnitude remains nonnegative because it represents overall size.
You can enter angular acceleration in rad/s², deg/s², or rev/s². Radius supports meters, centimeters, millimeters, feet, and inches. Angular velocity supports rad/s, deg/s, rpm, and rev/s.
The Plotly graph visualizes how tangential, centripetal, and total acceleration vary with radius or with angular acceleration. It helps compare growth trends and sensitivity quickly.
Yes. The calculator includes CSV and PDF export buttons. They save the summary metrics and the comparison table, which is useful for reports, class notes, or engineering documentation.
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.