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

Diameter = 120 cm. = 1.2 m.

Radius = 0.6 m.

Frequency = 1500 rpm.

= 1500/60 rps.

= 25 rps or s⁻¹

∵ ω = 2πf

∴ ω = 44/7 × 25

⇒ ω = 1100/7

ω = 157.14 rad/s.

Force = mrω²

⇒ F = 0.001 × 0.6 × (157.14)²

∴ F = 14.8 N.

The Force is exerted due to the friction on it. It is also due to the Inertial Property.

The Force which the particle exert on the blade along its surface is also will be same according to Newton's Third law of Motion.

Hope it helps.