Question

An automobile tire with a radius of 0.30 m starts at rest and accelerates at a constant angular acceleration of 2.0 rad/s2 for 5.0 s. What is the angular displacement of the tire?

Answer 1

Answer:

The value is $\theta = 25 \ radian$

Explanation:

From the question we are told that

   The radius is  $r = 0.30 \ m$

   The acceleration is $\alpha = 2.0 \ rad/s^2$

    The time taken is $t = 5.0$

Generally the angular displacement is mathematically represented as

          $\theta = \frac{s}{r}$

Here s is the linear distance covered by the tire which is mathematically represented as

        $s = u t + \frac{1}{2}a t^2$

Here  u is 0 given that the car started from rest and

               $a = \alpha * r = 2.0 * 0.30= 0.6\ m/s^2$

So

     $s = 0 + \frac{1}{2}*0.6* 5^2$

     $s = 7.5 \ m$      

So

      $\theta = \frac{7.5}{0.30}$

=>  $\theta = 25 \ radian$