← Describing rotation

Swap period and frequency

Sometimes the frequency is known and the period is the question: a fan spins at 4 Hz, and you want the time each revolution takes. f = 1/T works in both directions.

Start from the equation you know: f = 1/T.

Make T the subject: multiply both sides by T, then divide both sides by f.

That gives T = 1/f.

Both directions of the swapyou haveyou wantmovethe period Tthe frequency ff = 1/Tthe frequency fthe period TT = 1/f
Either way, divide 1 by the value you have.
The swap is the same move both ways: divide 1 by whichever of the two you have.

With f in hertz, T comes out in seconds; with T in seconds, f comes out in hertz.

The fan spins at 4 Hz. Calculate its period.

Write down the values:

f = 4 Hz, T = ?

Write down the equation:

T = 1/f

Substitute in the values, and calculate:

T = 1 / 4 = 0.25

The fan's period is 0.25 s.

A drone rotor has a period of 0.05 s. Calculate its frequency.

Write down the values:

T = 0.05 s, f = ?

Write down the equation:

f = 1/T

Substitute in the values, and calculate:

f = 1 / 0.05 = 20

The rotor's frequency is 20 Hz.

The two worked casesobjectgivenfoundfanf = 4 HzT = 0.25 sdrone rotorT = 0.05 sf = 20 Hz
The same division carries both cases.

Quick-fire drill

A pottery wheel spins at 2.0 Hz. Enter its period in s.

A hamster wheel has a period of 0.8 s. Enter its frequency in Hz.

A kitchen mixer whisk spins at 8.0 Hz. Enter its period in s.

A rotisserie spit has a period of 2.5 s. Enter its frequency in Hz.

A revolving sign turns with a period of 1.6 s. Enter its frequency in Hz.

A power drill's chuck spins at 50 Hz. Enter its period in s.

Your turn

During a slow bench test, a drone propeller spins at 10 Hz. Enter its period in s.

A bench grinder wheel has a period of 0.04 s. Enter its frequency in Hz.

At the park, a small merry-go-round completes exactly one fifth of a revolution each second, a frequency of 0.2 Hz. Enter its period in s.