What is the relationship between the frequency $f$ and the period $T$ in uniform circular motion?

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

Answer: (D)

Verified step by step guidance

1. Understand that in uniform circular motion, the period \(T\) is the time taken for one complete revolution or cycle.
2. Recognize that the frequency \(f\) is defined as the number of complete revolutions or cycles per unit time.
3. Since frequency is the reciprocal of the period, express this relationship mathematically as \(f = \frac{1}{T}\).
4. This means if the period increases, the frequency decreases, and vice versa, showing an inverse relationship.
5. Therefore, the correct formula relating frequency and period in uniform circular motion is \(f = \frac{1}{T}\).