Question

A ceiling fan is rotating at 0.96 rev/s. When turned off, it slows uniformly to a stop in 2.4 min. Calculate the angular acceleration of the fan and calculate the angle through which the fan blades rotate in this time.

Answer 1

We have the next information

ω_i= initial angular speed= 0.96 rev/s

ω_f= final angular speed= 0 rev/s

t=2.4 min= 144 s

We will use the next formula to calculate the angular acceleration

$\alpha=\frac{\omega_f-\omega_i}{t}=\frac{0.96-0}{144}=-0.006667rev/s^2$

Then we will use

$\theta=\omega_it+\frac{1}{2}\alpha t^2$$\theta=0.96(144)-\frac{1}{2}(0.0066)(144)^2=69.81\text{rev}$

Then we transform to degrees

1 rev =360°

$69.81\times360=25132.03\text{\degree}$

ANSWER

angular acceleration=-0.006667 rev/s^2

angle= 69.81 rev= 25132.03°