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. How much force does it experience when the fan runs at full speed ? Who exerts this force on the particle? How much force does the particle exert on the blade along its surface?

Answer 1

A ceiling fan has a diameter = 120 cm

$\therefore$ Radius, $r=60cm=0.6cm$

Mass of particle on the outer end of a blade is 1 g.

n = 1500 rev/min

= 25 rev/sec

$\omega =2\pi n=2\pi \times 25$

=157.14

Force of the particle on the blade

$=Mr{w}^2$

$=\left(0.001\right)\times 0.6\times (157.14{)}^2$

=14.8 N

The fan runs at a full speed in circular path. This exerts the force on the particle (inertia) the particle also exerts a force of 14.8 N on the blade along its surface.