Question

the initial angular velocity of a ceiling fan is 6.28 rad/s. it accelerates uniformly to 3.14 rad/s in 4.0 s. what is the angular acceleration? 0.39 rad/s² -0.79 rad/s² -0.39 rad/s² 0.79 rad/s²

Explanation:

Step1: Recall the formula for angular acceleration

The formula for angular acceleration \(\alpha=\frac{\omega_f - \omega_i}{t}\), where \(\omega_f\) is the final angular velocity, \(\omega_i\) is the initial angular velocity, and \(t\) is the time.

Step2: Substitute the given values

Given \(\omega_i = 6.28\space rad/s\), \(\omega_f=3.14\space rad/s\), and \(t = 4.0\space s\).
\(\alpha=\frac{3.14 - 6.28}{4.0}\)

Step3: Calculate the value

\(\alpha=\frac{- 3.14}{4.0}=- 0.785\approx - 0.79\space rad/s^{2}\)

Answer:

-0.79 rad/s²