Angular Velocity Calculator

Angular Velocity Calculator

Calculate angular velocity from angular displacement and time interval.

Calculate Angular Velocity

One full rotation = 2π ≈ 6.283185 rad

Time must be greater than zero

Angular Velocity

6.2832

rad/s

Frequency

1.0000

rev/s (Hz)

Rotational Speed

60.00

RPM

What is Angular Velocity?

Angular velocity measures how quickly an object rotates around a fixed axis. It is usually expressed in radians per second.

For uniform rotation, angular velocity is the angular displacement divided by the time taken. A larger angular displacement in the same time means a larger angular velocity.

Angular velocity is widely used in rotating machinery, wheels, motors, turbines, robotics, and general rotational dynamics.

How to Calculate Angular Velocity

The Basic Formula

ω = Δθ / Δt
ω = angular velocity (rad/s)
Δθ = angular displacement (rad)
Δt = time interval (s)

Useful Rotation References

Full rotation = 2π rad ≈ 6.283185 rad
Half rotation = π rad ≈ 3.141593 rad
Quarter rotation = π/2 rad ≈ 1.570796 rad

Conversions

Frequency: f = ω / 2π
RPM = f × 60 = (ω / 2π) × 60

Example Calculation

A wheel completes 3 full rotations in 6 seconds. What is its angular velocity?

Angular displacement:

Δθ = 3 × 2π = 6π ≈ 18.8496 rad

Angular velocity:

ω = 18.8496 / 6 ≈ 3.1416 rad/s

Convert to RPM:

RPM = (3.1416 / 2π) × 60 ≈ 30.00 RPM

Frequently Asked Questions

What's the difference between angular and linear velocity?

Angular velocity measures rotation rate, while linear velocity measures straight-line speed. They are related by v = ωr for a point at radius r.

Why are radians used?

Radians are the standard angular unit in physics because they make rotational formulas simpler and more natural.

Can angular velocity be negative?

Yes. The sign can represent direction of rotation, depending on the chosen sign convention.

How does angular velocity relate to frequency?

Frequency counts complete revolutions per second, while angular velocity counts radians per second. They are related by ω = 2πf.

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