← Angular velocity and the speed on the circle

Angular velocity

Bruno switches on a box fan. Each second, a blade sweeps through 720°: two full turns' worth of angle, every second.

That each-second sweep deserves a name of its own.

The angle an object sweeps out each second is called its angular velocity.

The symbol is the Greek letter ω, called omega.

Bruno's fan blade sweeps 720° each second, so its angular velocity is ω = 720° per second.

Bruno's fan blade, second by secondstopwatch timetotal angle swept1 s720°2 s1440°3 s2160°
720° arrives in every second: ω = 720° per second.

Angular velocity can be written in degrees per second, °/s, or in radians per second, rad/s.

You have compared sweep rates already: the object sweeping more angle each second was sweeping at the greater rate. Angular velocity is that rate's name.

A greater angular velocity means more angle swept in every second.

A microwave turntable sweeps 36° each second. What is its angular velocity?

Astrid says: 'A fan blade sweeping 540° each second has an angular velocity of 540° per second.' Is Astrid correct?

A carousel sweeps 30° each second. State its angular velocity.

The each-second sweep is 30°.

The carousel's angular velocity is ω = 30°/s.

A turbine rotor sweeps 4 radians each second. State its angular velocity.

Two more angular velocitiesobjecteach-second sweepangular velocitycarousel30°ω = 30°/sturbine rotor4 radiansω = 4 rad/s
Degrees per second or radians per second: either unit carries ω.

The each-second sweep is 4 radians.

The rotor's angular velocity is ω = 4 rad/s.

The same fan on its low settingsettingeach-second sweepangular velocityhigh720°ω = 720°/slow360°ω = 360°/s
The same fan, slower spin: a smaller each-second sweep is a smaller angular velocity.

Your turn

Four facts are recorded about a potter's wheel. Which one states its angular velocity?

Coral records a wheel's angular velocity. Which unit does she record?

A rotating sign has swept 1080° in total since opening time, and it sweeps 120° each second. Which value is the sign's angular velocity?

The angle an object sweeps out each second is called its ___.