Table of Contents
What Is Angular Velocity?
Angular velocity measures how fast an object rotates or revolves, expressed in radians per second (rad/s). It can also be expressed in revolutions per minute (RPM), degrees per second, or Hertz (cycles per second). It is the rate of change of angular position with respect to time.
Angular velocity applies to wheels, gears, motors, turbines, planets, spinning tops, centrifuges, and any rotating system. It relates to linear velocity through the formula v = omega * r, where r is the distance from the rotation axis. Points farther from the axis move faster for the same angular velocity.
Conversion Formulas
Where omega is angular velocity in rad/s, f is frequency in Hz, T is period in seconds, v is tangential velocity, and r is radius.
Common Angular Velocities
| Object | RPM | rad/s |
|---|---|---|
| Earth rotation | 0.000694 | 7.27e-5 |
| Clock minute hand | 0.0167 | 0.00175 |
| Car wheel (60 mph) | ~840 | 88 |
| Hard drive | 7,200 | 754 |
| Dental drill | 400,000 | 41,888 |
| Neutron star | up to 43,000 | 4,500 |
FAQ
What is the difference between RPM and rad/s?
RPM counts complete revolutions per minute. Rad/s measures radians per second, where one revolution = 2 pi radians. Multiply RPM by 2*pi/60 to get rad/s. Rad/s is the standard SI unit used in physics equations.
How does angular velocity relate to linear speed?
The tangential (linear) speed of a point on a rotating object equals omega times its distance from the axis: v = omega*r. The rim of a spinning wheel moves faster than a point near the hub, even though both have the same angular velocity.
Can angular velocity be negative?
Yes. The sign of angular velocity indicates direction of rotation. By convention, counterclockwise rotation (viewed from above) is positive, and clockwise is negative. The right-hand rule gives the direction of the angular velocity vector along the rotation axis.