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 1g sticking at the outer end of a blade. What is the net force on it, when the fan runs at full speed ? Who exerts this force on the particle ? How much force does the particle exert on the blade in the plane of motion ?
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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 1g sticking at the outer end of a blade. What is the net force on it, when the fan runs at full speed ? Who exerts this force on the particle ? How much force does the particle exert on the blade in the plane of motion ?

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G1 Physics · Accepted Answer

Radius is 0.6 m and 1500 rpm=25 rps, so ω=50π rad/s. Centripetal force=mω²r=0.001(50π)²(0.6)=1.5π²≈14.8 N. It is exerted by the blade; by Newton's third law the particle exerts equal and opposite force on the blade.