Question

A Fan is rotating with a speed if 450 rev/min. After being switched off it comes to rest in 10s. Assuming constant angular deceleration,Calculate the number of revolutions made by it before coming to rest.

Answer 1

Consider (•) = nought ok!☺

Here; f• = 450 rev/ min = 450 rev/s

60

f• = 15 rev/s

2

Therefore the angular velocity ω• = 2π f•

= 15π rad / sec at t= 10s, ω = 0

Therefore Angular acceleration

α = ω - ω•

t

= 0- 15π = -15 π = - 3π rad / s^2

10 s 10 2

Φ = ω• + 1/2 αt^2

= 15π * 10 - 1/2 (3π/2) 10^2

= 150π -75π = 75 π rad

Therefore No. of revolution = Φ = 75

2π 2π

= 37.5

Therefore The fan will make 37.5 no of revolution before commong to rest...

Answer 2

Consider (•) = nought

Here; f• = 450 rev/ min = 450 rev/s

60

f• = 15 rev/s

2

Therefore the angular velocity ω• = 2π f•

= 15π rad / sec at t= 10s, ω = 0

Therefore Angular acceleration

α = ω - ω•

t

= 0- 15π = -15 π = - 3π rad / s^2

10 s 10 2

Φ = ω• + 1/2 αt^2

= 15π * 10 - 1/2 (3π/2) 10^2

= 150π -75π = 75 π rad

Therefore No. of revolution = Φ = 75

2π 2π

= 37.5

Therefore The fan will make 37.5 no of revolution before commong to rest...

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