Rotational Equilibrium and Rotational Dynamics

Question

You turned on your classroom ceiling fan at its lowest setting. You measured that the rotation is 250 rev/min. When adjusted to its maximum setting, the speed increases to 450 rev/min in 15 s. (a) What is the angular acceleration of the blades? (b) How many revolutions do the blades go through while accelerating? USE THE GUESS METHOD

Answer 1

Angular acceleration is normally measured redians per second.

But the angular velocities are given in rev/min, so I assume you want the

same units for the acceleration.

Let

ω₀ = 250 rev/min be the initial angular velocity,

ω₁ = 450 rev/min be the final angular velocity,

t = 15 s = (1/4) min be the time it took to change from ω₀ to ω₁,

α (to be computed) be the angular acceleration.

(a)

I am guessing that the acceleration is constant during the change of speed.

In that case

α = (ω₁ - ω₀)/t = (200 rev/min)/(1/4 min) = 800 rev/min²

(b)

The number of revolutions is given by the formula

ω₀t + αt²/2 = 250 rev/min × (1/4) min + 800 rev/min² × (1/4 min)² / 2 = 87.5 rev