Question

Define period and frequency of particle performing uniform circular motion. State their S.I. units.

Answer 1

Hint: Uniform circular motion is defined as a motion of the body in which the object completes repeated motion around the same path in the same amount of time. It is a periodic motion with definite frequency and period.

Complete step by step answer:
A uniform circular motion is characterized by few parameters such as time period, frequency, phase, amplitude etc.
Total amount of time taken by an object to complete one revolution is called Period. The object in that time completes the revolution of a circular path. It is the minimum time after which the object repeats its motion on its own. It is denoted by T. As it defines time, it has units of time. Thus, S.I. unit of period is second.
Frequency is defined as the number of rotations in unit time. It is denoted as f or $\nu$. It is the inverse of time period. S.I. unit of frequency is rotations per second or Hertz (Hz). A wave vibrating frequently has a low speed. And a wave vibrating with a low frequency has high speed.
Frequency and time period are distinct yet related quantities. Period is seconds per cycle while frequency is cycles per second.
The relation between frequency and time period is given by,
$f={\displaystyle \frac{1}{T}}$ Or $T={\displaystyle \frac{1}{f}}$
Regular frequency is also related to the angular frequency ($\mathrm{\Omega }$).
$f={\displaystyle \frac{\mathrm{\Omega }}{2\pi }}$

Note: Period is independent of amplitude, energy and phase. Acceleration of the body is directly proportional to displacement of the particle or body from equilibrium. During this displacement, amplitude remains constant. Rotation of blades of a ceiling fan is an example of uniform circular motion.