Period, frequency and angular velocity

When a body travels a circular trajectory of radius $r$ at constant speed, we speak of uniform circular motion. Describing it requires new quantities, linked to the periodicity of the motion.

Quantities of circular motion (periodicity)

• Period $T$: time for one complete revolution (s);
• Frequency $f = \dfrac{1}{T}$: number of revolutions per second (Hz);
• Angular velocity $\omega = \dfrac{2\pi}{T}$: angle swept per unit time (rad/s).

Period and frequency are the inverse of one another: if a revolution takes $T = 0{,}5\;\text{s}$, then $f = 2$ revolutions occur in one second. Angular velocity $\omega$, instead, measures how quickly the radius joining the body to the centre rotates: in one complete period the radius sweeps out the full angle $2\pi$, hence $\omega = 2\pi/T = 2\pi f$.

$T = \frac{2\pi}{\omega}$

These three quantities describe the “cadence” of the motion — how often the body returns to the same point — but not yet how fast it moves along the circumference: for that we need to relate $\omega$ to the radius, as in the next atom.

Collegamenti

Argomenti: Cinematica Concetti: Moto circolare uniforme · Velocità angolare

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