What this calculator does
Angular Acceleration works out rate of change of angular velocity over a time interval, from spin-up or spin-down. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulaα = (ω₂ − ω₁) / t
The inputs explained
| Field | What to enter |
|---|---|
| Initial angular velocity (ω₁) (rad/s) | A number, measured in rad/s. Starts at 0. |
| Final angular velocity (ω₂) (rad/s) | A number, measured in rad/s. Starts at 12. |
| Time interval (s) | A number, measured in s. Starts at 4. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with initial angular velocity (ω₁)
Every other input is held at the calculator’s starting values while initial angular velocity (ω₁) varies. Select any row to load that scenario into the calculator.
How the answer changes with initial angular velocity (ω₁)
| Initial angular velocity (ω₁) (rad/s) | Angular acceleration (α) | Change in angular velocity | Direction |
|---|---|---|---|
| 1 | 2.750 rad/s² | 11.000 rad/s | Speeding up (positive) |
| 2 | 2.500 rad/s² | 10.000 rad/s | Speeding up (positive) |
| 5 | 1.750 rad/s² | 7.000 rad/s | Speeding up (positive) |
| 10 | 0.5000 rad/s² | 2.000 rad/s | Speeding up (positive) |
| 20 | -2.000 rad/s² | -8.000 rad/s | Slowing down (negative) |
| 50 | -9.500 rad/s² | -38.000 rad/s | Slowing down (negative) |