Question

A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of 120 cm and rpm 1500 at full speed. Consider a particle of mass 1 g sticking at the outer end of a blade.
a. How much force does it experience when the fan runs at full speed?
b. Who exerts this force on the particle?
c. How much force does the particle exert on the blade along its surface?

Answer 1

Diameter $=2R=120cm=120\times {10}^{-2}m$

$Rpm=1500$

Revolution per second $=\frac{1500}{60}=25$

Angular velocity $w=25\times 2\pi =50\pi rad/s$

$a)$ Force $=mr{w}^2$

$=1\times {10}^{-3}\times 60\times {10}^{-3}\times 2500{pi}^2$

$=14.8N$

$b)$ The fan exerts this force on the particle.

$c)$ By Newton's third law the particle also exert $14.8N$ of force on the blade along its surface.