Angular velocity

\omega=\dfrac{2\pi}{T}=2\pi f

Result unit: rad/s

What it describes

Angular velocity — the angle swept out per unit of time during circular motion.

\omega

angular velocity

[rad/s]

T

period of revolution

[s]

f

frequency

[Hz]

In one period

T

the body sweeps out a full angle of

2\pi

rad, so the angular velocity is

2\pi/T

. Since

f=1/T

, we also have

\omega=2\pi f

Circular and rotational motion — it links the period, the frequency and the angular velocity.

A wheel rotates at a frequency of

f=2

Hz. Find its angular velocity.

Substitution

f=2

Hz.

Result

\omega=2\pi\cdot2\approx12.6

rad/s.

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