Question

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2. In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval

Answer 1

Answer:

The  time interval is  $t = 3 \ s$

Explanation:

From the question we are told that

    The angular acceleration is  $\alpha = 4.0 \ rad/s^2$

     The  time taken is  $t = 4.0 \ s$

      The angular displacement is  $\theta = 80 \ radians$

     

The angular displacement can be represented by the second equation of motion as shown below

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

where  $w_i$ is the initial velocity at the start of the 4 second interval

So substituting values

        $80 = w_i * 4 + 0.5 * 4.0 * (4^2)$

=>    $w_i = 12 \ rad/s$

Now considering this motion starting from the start point (that is rest ) we have

       $w__{4.0 }} = w__{0}} + \alpha * t$

Where  $w__{0}}$ is the angular velocity at rest which is zero  and  $w__{4}}$ is the angular velocity after 4.0 second which is calculated as 12 rad/s s

        $12 = 0 + 4 t$

=>       $t = 3 \ s$