Solve rotational change using multiple physics input methods. Switch units, inspect steps, and test examples. Download reports and graph angular trends with clean outputs.
| Case | Input Set | Method | Angular Acceleration |
|---|---|---|---|
| Lab flywheel | 5 to 17 rad/s in 4 s | Velocity and time | 3 rad/s² |
| Motor startup | 120 to 720 rpm in 6 s | RPM and time | 10.472 rad/s² |
| Rotor with torque | 24 N·m and 3 kg·m² | Torque and inertia | 8 rad/s² |
| Turntable motion | ω₀ = 2 rad/s, θ = 30 rad, t = 4 s | Displacement and time | 2.75 rad/s² |
| Spin-up test | 3 to 11 rad/s across 14 rad | Velocity and displacement | 4 rad/s² |
1. α = (ωf − ωi) / t
2. α = τ / I
3. α = Δω / t after converting rpm to rad/s
4. α = 2(θ − ω₀t) / t²
5. α = (ω² − ω₀²) / 2θ
Here, α is angular acceleration, ω is angular velocity, t is time, θ is angular displacement, τ is torque, and I is moment of inertia.
Choose the calculation mode that matches the data you already have.
Enter the known values and select the correct units for each field.
Add graph duration and point count if you want a longer motion plot.
Press Calculate to show the result above the form.
Review the converted outputs, the formula used, and the step list.
Use the CSV and PDF buttons to save the result summary.
Angular acceleration describes how quickly angular velocity changes with time. It is a core rotational motion quantity in physics, engineering, and machine analysis. Positive values show spin speeding up in the chosen direction, while negative values show slowing down or acceleration opposite the chosen direction.
Different problems provide different known values. Some give initial and final angular velocity with time. Others provide torque and moment of inertia. Rotational kinematics can also use angular displacement with time, or displacement with starting and ending angular speed. This calculator supports all of these common routes in one place.
Unit conversion matters because rotational data often appears in radians per second, degrees per second, revolutions per second, or rpm. The calculator standardizes the math in SI form and then reports equivalent outputs in several useful units. That makes comparison easier when reading lab work, classroom problems, rotor tests, and machinery specifications.
The graph is useful for checking how angular velocity and displacement evolve under constant angular acceleration. This visual step can reveal unrealistic assumptions, confirm direction changes, and help explain motion during reports, homework, or design reviews.
Angular acceleration measures how fast angular velocity changes over time. It is the rotational counterpart of linear acceleration and is commonly written as α.
Radians per second squared is the standard physics unit. This calculator also shows equivalent values in degrees per second squared, revolutions per second squared, and rpm per second.
Yes. A negative result means angular velocity decreases in the chosen positive direction, or the object accelerates in the opposite rotational direction.
Use that method when torque and moment of inertia are known. It is especially useful for motors, flywheels, shafts, and rotating assemblies under applied torque.
Unit conversion keeps the physics consistent. Mixing rpm, degrees, minutes, and SI values without conversion can produce incorrect angular acceleration results.
The graph plots angular velocity and angular displacement over the selected duration, assuming constant angular acceleration based on your calculated result and starting conditions.
You also need a starting angular velocity or another motion quantity. Displacement and time alone are not enough to determine a unique constant angular acceleration.
Yes. Use the CSV button for tabular export and the PDF button for a downloadable report version of the current result section.
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.