Question

3. Christina is on her college softball team, and she is practicing swinging the bat. Her coach wants her to work on the speed and acceleration of her swing. She has a device that measures the linear velocity of the bat during the swing. Her bat is 0.85 m long. On her first swing, the linear velocity of the bat just prior to the swing is 0 m/s, and 0.15 s later, just prior to ball contact is 16 m/s. What is the average angular acceleration of the end of her bat during the swing?

Answer 1

Answer:

The average angular acceleration is  $\alpha =125.487 rad /s^2$

Explanation:

From the question we are told that

  From the question we are told that

        The length of the bat is $l = 0.85m$  \

         The initial linear velocity is  $u = 0 m/s$

         The time is  $t = 0.15s$

         The velocity at t is  $v = 16 m/s$

  Generally average  angular acceleration is mathematically represented as

                $\alpha = \frac{w_f - w_o}{t}$

        Where $w_f$ is the finial angular velocity which is mathematically evaluated as  

            $w_f = \frac{v}{l}$

                  $w_f = \frac{16}{0.85}$

                        $= 18.823 rad/s$

 and $w_o$ is the initial angular velocity which is zero since initial linear velocity is zero

               So

                         $\alpha = \frac{18.823 - 0}{0.15}$

                               $\alpha =125.487 rad /s^2$