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

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

Answer: (A)

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 the relationship between period and frequency: Since frequency is how many cycles occur in one second, and period is how long one cycle takes, they are inversely related.
3. Express this inverse relationship mathematically as \(T = \frac{1}{f}\), meaning the period is the reciprocal of the frequency.
4. Verify the units: Frequency \(f\) is measured in hertz (Hz), which is cycles per second, and period \(T\) is measured in seconds, so \(T = \frac{1}{f}\) makes sense dimensionally.
5. Conclude that the correct formula relating period and frequency in uniform circular motion is \(T = \frac{1}{f}\).