The speed the fan will turn is 625 rpm
Linear speed
Since they fan and the pulley ahve the same linear speed v = rω where
- r = radius of pulley and
- ω = angular speed.
Then
r₁ω₁ = r₂ω₂ where
- r₁ = radius of fan pulley = 8 in/2 = 4 in,
- ω₁ = angular speed of fan pulley,
- r₂ = radius of motor pulley = 4 in/2 = 2 in,
- ω₂ = angular speed of motor pulley = 1250 rpm
Angular speed of fan pulley
Making ω₁ subject of the formula, we have
ω₁ = r₂ω₂/r₁
Substituting the values of the variables into the equation, we have
ω₁ = r₂ω₂/r₁
ω₁ = 2 in × 1250 rpm/4 in
ω₁ = 1250 rpm/2
ω₁ = 625 rpm
So, the speed the fan will turn is 625 rpm
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