Calculator Inputs
Example Data Table
| Method | Input Example | Angular Velocity |
|---|---|---|
| Angle/Time | 720 deg in 4 s | 3.141593 rad/s |
| Frequency | 2 Hz | 12.566371 rad/s |
| RPM | 120 rpm | 12.566371 rad/s |
| Period | 0.5 s | 12.566371 rad/s |
| v and r | 10 m/s, 0.5 m | 20.000000 rad/s |
| ac and r | 25 m/s², 0.5 m | 7.071068 rad/s |
Formula Used
ω = θ / tUse when you know angular displacement and elapsed time.
ω = 2πfFrequency in hertz converts directly to radians per second.
ω = 2πN / 60Useful for motors, fans, pulleys, and rotating shafts.
ω = 2π / TChoose this when one full rotation time is known.
ω = v / rRequires tangential speed and radius in consistent units.
ω = √(ac / r)Derived from ac = ω²r for circular motion.
How to Use This Calculator
- Select the solve mode that matches the values you already know.
- Enter the input numbers and choose the proper units.
- Pick the rotation direction to control the sign.
- Set significant figures and graph end time if needed.
- Press the calculate button to show results below the header.
- Review converted values, the summary table, and the graph.
- Use the export buttons to save CSV or PDF output.
Frequently Asked Questions
1) What is angular velocity?
Angular velocity measures how fast an object rotates around an axis. It describes the rate of change of angular displacement, usually in radians per second.
2) What unit is commonly used for angular velocity?
The standard SI unit is radians per second. This calculator also shows degrees per second, revolutions per second, RPM, frequency, and period.
3) How is angular velocity different from frequency?
Frequency counts rotations each second, while angular velocity measures rotation rate in radians each second. They are related through ω = 2πf.
4) Can angular velocity be negative?
Yes. The sign indicates direction. Positive often represents counterclockwise rotation, while negative often represents clockwise rotation in a chosen coordinate system.
5) How do I calculate angular velocity from RPM?
Multiply RPM by 2π, then divide by 60. That converts revolutions per minute into radians per second for physics calculations.
6) Why is radius optional in some modes?
Radius is only needed when linear motion information is involved. If you already know angle, time, frequency, RPM, or period, radius is unnecessary.
7) What does the graph show?
The graph plots angular displacement versus time using the calculated angular velocity. It helps you visualize how rotation accumulates over the selected time span.
8) When should I use period instead of frequency?
Use period when one full cycle time is easier to measure. Use frequency when you already know cycles per second directly.