In uniform circular motion, what is the relationship between the frequency $f$ and the period $T$?

• A. $f=\frac{T}{1}$
• B. $f=2\pi T$
• C. $f=T$
• D. $f=\frac{1}{T}$

Answer: (D)

Verified step by step guidance

1. Understand the definitions: The period \(T\) is the time taken for one complete revolution in uniform circular motion, while the frequency \(f\) is the number of revolutions per unit time.
2. Recall that frequency and period are inversely related because if it takes longer to complete one revolution (larger \(T\)), fewer revolutions occur per second (smaller \(f\)).
3. Express this inverse relationship mathematically as \(f = \frac{1}{T}\), meaning frequency is the reciprocal of the period.
4. Verify the units: period \(T\) is measured in seconds (s), so frequency \(f\) is measured in hertz (Hz), which is equivalent to \(\text{s}^{-1}\).
5. Conclude that the correct formula relating frequency and period in uniform circular motion is \(f = \frac{1}{T}\).