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

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

Answer: (B)

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 measures how many cycles occur in one second, and period measures how long one cycle takes, they are inversely related.
3. Express this inverse relationship mathematically: \(f = \frac{1}{T}\), meaning frequency is the reciprocal of the period.
4. Similarly, the period can be expressed as the reciprocal of the frequency: \(T = \frac{1}{f}\).
5. Therefore, the correct relationship is that frequency equals one divided by the period, not frequency equals the period squared or frequency equals the period.