How to use the rotational kinematics calculator
Find final angular velocity and angle turned under constant angular acceleration. Enter initial angular velocity, angular acceleration, time in the fields above; the final angular velocity, angle turned, revolutions are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- w0 — Initial angular velocity (rad/s)
- alpha — Angular acceleration (rad/s²)
- t — Time (s)
Worked example
With initial angular velocity = 0 rad/s, angular acceleration = 4 rad/s², time = 6 s, the calculator gives final angular velocity ≈ 24 rad/s; angle turned ≈ 72 rad; revolutions ≈ 11.45916 rev.
Frequently asked questions
What is the formula for the rotational kinematics calculation?
Final angular velocity (rad/s) = w0+alpha × t. Angle turned (rad) = w0 × t+0.5 × alpha × t × t. Revolutions (rev) = [Angle turned] / (2 × π). Here w0 is initial angular velocity (rad/s), alpha is angular acceleration (rad/s²), t is time (s).
What inputs do I need for the rotational kinematics calculator?
You need initial angular velocity in rad/s, angular acceleration in rad/s², time in s. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.