Define the period and frequency of revolution of a particle performing

1.	Define the period and frequency of revolution of a particle performing uniform circular motion (UCM) and state expressions for them. Also state their SI units.
Answer» (1) Period of revolution : The time taken by a particle performing UCM to complete one revolution is called the period of revolution or the period (T) of UCM. T = \(\frac{2\pi r}v\) = \(\frac{2 \pi}{\omega}\) where v and ω are the linear and angular speeds, respectively. SI unit: the second (s) Dimensions : [M°L°T¹]. (2) Frequency of revolution : The number of revolutions per unit time made by a particle in UCM is called the frequency of revolution (f). The particle completes 1 revolution in periodic time T. Therefore, it completes 1/T revolutions per unit time ∴ Frequency f = \(\frac1T\) = \(\frac{v}{2 \pi r}\) = \(\frac{\omega}{2 \pi }\) SI unit : the hertz (Hz), 1 Hz = 1 s^-1 Dimensions : [M°L°T^-1]

Define the period and frequency of revolution of a particle performing uniform circular motion (UCM) and state expressions for them. Also state their SI units.

Answer»

(1) Period of revolution : The time taken by a particle performing UCM to complete one revolution is called the period of revolution or the period (T) of UCM.

T = \(\frac{2\pi r}v\) = \(\frac{2 \pi}{\omega}\)

where v and ω are the linear and angular speeds, respectively.

SI unit: the second (s)

Dimensions : [M°L°T¹].

(2) Frequency of revolution : The number of revolutions per unit time made by a particle in UCM is called the frequency of revolution (f).

The particle completes 1 revolution in periodic time T. Therefore, it completes 1/T revolutions per unit time

∴ Frequency f = \(\frac1T\) = \(\frac{v}{2 \pi r}\) = \(\frac{\omega}{2 \pi }\)

SI unit : the hertz (Hz), 1 Hz = 1 s^-1

Dimensions : [M°L°T^-1]

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