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?

Step-by-step solution

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       &