When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many rotations will it make before coming to rest?

Question

When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many rotations will it make before coming to rest?, 24, 36, 18, 12

MARKS App · Accepted Answer

From the third equation of angular motion, ω 2 = ω 0 2 - 2 αθ ( H e r e , ω = ω 0 2 , θ = 36 × 2 π ) ∴ ω 0 2 2 = ω 0 2 - 2 α × 36 × 2 π or 4 × 36 π α = ω 0 2 - ω 0 2 4 or 4 × 36 π α = 3 ω 0 2 4 or α = ω 0 2 16 × 12 π ...(i) According to question again applying the third equation of angular motion ω 2 = ω 0 2 - 2 α θ ( H e r e , ω = 0 ) ∴ 0 = ω 0 2 2 - 2 × ω 0 2 . θ 16 × 12 π or θ = 24 π o r θ = 12 × 2 π But 2 π = 1 cycle So, θ = 12 c y c l e

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