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# A ceiling fan has diameter (the circle through the outer edge of the blade) of 120cm and 1500rpm at full speed. Consider a particle of mass 1 g stick at the outer edge of the blade. How much force does it experience when the fun runs at full speed?

Last updated date: 01st Mar 2024
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Hint: We need to understand the relation between the distance of the particle from the center of rotation, the mass of the particle and the rotational speed of the fan to find the force acting on the particle situated on the fan blade while it is rotating.

We know that any rotating body has a torque acting at each point from the center of rotation, which is dependent on the distance from the center. The force acting on a particle of mass ‘m’ at a distance of ‘r’ from the center of rotation rotating with an angular velocity of $\omega$ can be given as –
$F=m{{\omega }^{2}}r$
\begin{align} & f=\dfrac{1500}{60}rps=25rps \\ & \Rightarrow \omega =2\pi 25rad{{s}^{-1}} \\ & \therefore \omega =50\pi rad{{s}^{-1}} \\ \end{align}
\begin{align} & F=m{{\omega }^{2}}r \\ & \Rightarrow F={{10}^{-3}}kg\times {{(50\pi )}^{2}}\times 0.6 \\ & \therefore F=14.8N \\ \end{align}