In uniform circular motion, what is the correct relationship between the period and the frequency of rotation?

• A. The period is the time for one revolution and the frequency is the number of revolutions per second; they are related by $f=\frac{1}{T}$.
• B. The period is the number of revolutions per second and the frequency is the time for one revolution; they are related by $T=\frac{1}{f}$.
• C. The period and frequency are the same quantity measured in different units, so $f=T$.
• D. The period is the time for one revolution and the frequency is the angular speed; they are related by $f=\omega$.

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, measured in seconds.
2. The frequency \(f\) is the number of complete revolutions per second, measured in hertz (Hz).
3. Since frequency counts how many revolutions happen in one second, and period measures how long one revolution takes, they are inversely related.
4. Express this inverse relationship mathematically as \(f = \frac{1}{T}\), meaning frequency is the reciprocal of the period.
5. Similarly, you can write the period in terms of frequency as \(T = \frac{1}{f}\), showing that the period is the reciprocal of the frequency.