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?
Given parameters:
Diameter, d = 120 cm = 1.2 m
Radius, r = d/2 = 0.6 m
Frequency, f = 1500 rpm (rotations per minute)
= 1500/60 rps (rotations per second)
= 25 s-1
Angular frequency, ω = 2πf = 2 × 3.14 × 25
= 157.14 rad s-1
Mass of the particle, m = 1g =0.001 kg
Force on the particle = mrω2
= 0.001 × 0.6 × 157.14 ×157.14
= 14.81 N
This force is exerted by factors like friction, air drag and inertia.
Force exerted by the particle on the blade = Force exerted on the particle = 14.81 N