#### 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?

#### Solution

Diameter of the fan = 120 cm

∴ Radius of the fan = r = 60 cm = 0.6 m

Mass of the particle = M = 1 g = 0.001 kg

Frequency of revolutions = n = 1500 rev/min = 25 rev/s

Angular velocity = ω = 2\[\pi\]n = 2\[\pi\] × 25 = 57.14 rev/s

Force of the blade on the particle:

F = Mrw^{2}

= (0.001) × 0.6 × (157.14)^{2}

=14.8 N

The moving fan exerts this force on the particle.

The particle also exerts a force of 14.8 N on the blade along its surface.