Question

Write the formula of centrifugal force in terms of frequency.

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Answer 1

Question

Write the formula of centrifugal force in terms of Frequency

Solution

Centrifugal force is generally given as :

$\sf F = \dfrac{mv^2}{r}$

Centrifugal forces generally act on revolving objects. Thus,the terms time period and frequency come into the picture.

The distance covered by the object would be 2πr

Velocity of the object would be :

$\sf \: v = \dfrac{2\pi \: r}{T}$

But $\sf \: T = \dfrac{1}{f}$

Thus,

$\implies \ \boxed{ \boxed{ \sf{v = 2\pi \: rf}}}$

$Here \begin{cases} \sf{v \longrightarrow Velocity} \\ \sf{T \longrightarrow Time \ Period} \\ \sf{f \longrightarrow Frequency} \end{cases}$

Centrifugal Force would be :

$\sf F = m \times (2 \pi rf)^{2} \dfrac{1}{r} \\ \\ \huge{ \longrightarrow \boxed{\boxed{\sf F = 4 \pi^2 r m f^2}}}$