Question

A fan blade, initially at rest, rotates with a constant acceleration of 0.029 rad/s2. What is the time interval required for it to reach a 6.58-rad displacement after starting from rest

Answer 1

Answer:

The time interval is  $t = 21.30 \ s$

Explanation:

From the question we are told that

    The constant acceleration is $\alpha = 0.029 \ rad / s^2$

    The displacement is  $\theta = 6.58 \ rad$

     

According to the second equation of motion we have that

    $\theta = w_i* t + \frac{1}{2} * \alpha t^2$

given that the blade started from rest

     $w_i$ which is the initial angular velocity is 0

 So  

       $\theta = 0 + \frac{1}{2} * \alpha t^2$

 =>  $t = \sqrt{ \frac{2 * \theta }{\alpha } }$

substituting values  

=>    $t = \sqrt{ \frac{2 * 6.58 }{0.029 } }$

=>    $t = 21.30 \ s$