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.
Q 12
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(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.
$
\mathrm{T}=\frac{2 \pi r}{v}=\frac{2 \pi}{\omega}
$
where $v$ and $w$ are the linear and angular speeds, respectively.
SI unit: the second (s)
Dimensions : $\left[\mathrm{M}^{\circ} \mathrm{L}^{\circ} \mathrm{T}^1\right]$.
(2) Frequency of revolution: The number of revolutions per unit time made by a particle in UCM is called the frequency of revolution ( $f$ ).
$
\mathrm{T}=\frac{2 \pi r}{v}=\frac{2 \pi}{\omega}
$
where $v$ and $w$ are the linear and angular speeds, respectively.
SI unit: the second (s)
Dimensions : $\left[\mathrm{M}^{\circ} \mathrm{L}^{\circ} \mathrm{T}^1\right]$.
(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.
$\therefore$ Frequency $\mathrm{f}=\frac{1}{T}=\frac{v}{2 \pi r}=\frac{\omega}{2 \pi}$
SI unit : the hertz $(\mathrm{Hz}), 1 \mathrm{~Hz}=1 \mathrm{~s}^{-1}$
Dimensions: $\left[\mathrm{M}^{\circ} \mathrm{L}^{\circ} \mathrm{T}^{-1}\right]$
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