Question

A ceiling fan has a diameter of the circle through the outer edges of the three blades of $120cm$ and rpm $1500$ at full speed. Consider a particle of mass $1g$ sticking at the outer end of the blade. What is the net force on it, when the fan runs at full speed? Who exerts this force on the particle? How much force does the particle exert on the blade in the plane of motion?

Answer 1

Radius, $r=\frac{120}{2}$ $cm=60\times {10}^{-2}$ $m$

Angular velocity, $\omega =1500$ $rpm$

$⟹\omega =\frac{1500}{60}$ $rps$

$⟹\omega =25$ $rps$

$⟹\omega =25\times 2\pi$ $rad/s$

$⟹\omega =50\pi$ $rad/s$

Net force on the particle:

$T=mr{\omega }^2$

$⟹T={10}^{-3}\times 60\times {10}^{-2}\times 2500{\pi }^2$

$⟹T=1.5{\pi }^2$

$⟹T=14.8$ $N$

From Newton's third law of motion, the particle also exerts $14.8$ $N$ of force on the blade in the plane of motion.