Angular Velocity Calculator
Calculate angular velocity, linear velocity, or radius using ω = v / r. Select the calculation mode below.
Related: | | |
What is Angular Velocity?
Angular velocity is a measure of how fast an object rotates or revolves around a fixed axis. It represents the rate of change of angular displacement over time. The relationship between angular velocity and linear velocity is:
ω = v / r
Where ω (omega) is angular velocity in rad/s, v is linear (tangential) velocity in m/s, and r is the radius of rotation in meters. Angular velocity is a vector quantity following the right-hand rule — the direction is along the axis of rotation.
Common Angular Velocity Reference Values
| Object / Event | ω (rad/s) |
|---|---|
| Earth's rotation | 0 |
| CD/DVD spinning (read) | 52.4 |
| Car engine idle (700 rpm) | 73.3 |
| Hard drive 7200 RPM | 754 |
| Bicycle wheel (20 km/h) | 41.9 |
| Wind turbine (typical) | 1.57 |
| Turbocharger (max) | 10,472 |
| Second hand of clock | 0.105 |
Related Calculators
Authoritative References
Frequently Asked Questions
What is angular velocity?
Angular velocity is a vector quantity that measures the rate of rotation of an object around an axis. It describes how quickly an object rotates or revolves, defined as angular displacement per unit time. The formula is ω = v / r, where ω is angular velocity, v is linear (tangential) velocity, and r is the radius of rotation.
How do I calculate angular velocity?
Angular velocity is calculated by dividing linear velocity by the radius: ω = v / r. For example, a point on a 0.5 m radius wheel moving at 10 m/s has angular velocity ω = 10 / 0.5 = 20 rad/s. Alternatively, ω = 2πf, where f is the rotational frequency in hertz (revolutions per second).
What units are used for angular velocity?
Common units include: radians per second (rad/s) — the SI unit; revolutions per minute (RPM) — commonly used for engines and motors; degrees per second (°/s) — used in navigation; and revolutions per second (rps). One full revolution equals 2π radians or 360 degrees.
What is the relationship between angular and linear velocity?
Linear (tangential) velocity is related to angular velocity by v = ω × r, where r is the radius. A point farther from the center of rotation moves faster than a point closer to the center, even though both have the same angular velocity. This explains why the outer edge of a merry-go-round moves faster than the center.
What is the difference between angular velocity and angular acceleration?
Angular velocity (ω) is the rate of angular displacement, while angular acceleration (α) is the rate of change of angular velocity: α = Δω / t. Angular acceleration occurs when rotational speed changes, such as when an engine revs up or a spinning top slows down due to friction.
How is angular velocity used in real-world applications?
Angular velocity is essential in: automotive engineering (engine RPM, wheel speed), robotics (joint rotation speeds), satellite tracking (antenna rotation), centrifuges (separation speed), wind turbines (blade rotation), audio equipment (turntables, hard drives), and aerospace (gyroscopes, spacecraft attitude control).