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Question
A ceiling fan has a moment of inertia of 2 kg. m2. It attains maximum frequency of 60 r.p.m. in 2π seconds. Calculate its power rating.
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Solution
Given:
Moment of inertia (I) = 2 kg. m2
Maximum frequency = 60 rpm = 1 rps
Time (t) = 2π s
Angular velocity (ω) = 2π f
= 2π(1)
= 2π rad/s
Angular acceleration (α) = `omega/t`
= `(2 pi)/(2 pi)`
= 1 rad/s2
Torque (τ) = Iα
= 2(1)
= 2 N m
Power (P) = τω
= 2 × 2π
= 4π W
= 12.57 W
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