Question

The blades of a fan running at low speed turn at 250 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 350 rpm in 5.75 seconds. What is the magnitude of the angular acceleration of the blades in rad/s2?

Answer 1

Answer:

1.82 rad/s².

Explanation:

Applying,

α = (ω₂-ω₁)/t..................... Equation 1

Where α = angular acceleration of the fan blades, ω₂ = final angular velocity of the fan blades, ω₁ = initial angular velocity of the fan blades, t =  time.

Given: ω₂ = 350 rpm = (350×0.1047) rad/s = 36.645 rad/s. ω₁ = 250 rpm = (250×0.1047) rad/s = 26.175 rad/s, t = 5.75 s.

Substitute into equation 1

α = (36.645-26.175)/5.75

α = 10.47/5.75

α = 1.82 rad/s².

Hence the magnitude of the angular acceleration of the fan blades = 1.82 rad/s²