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?

Respuesta :

Answer:

The average angular acceleration is  [tex]\alpha =125.487 rad /s^2[/tex]

Explanation:

From the question we are told that

  From the question we are told that

        The length of the bat is [tex]l = 0.85m[/tex]  \

         The initial linear velocity is  [tex]u = 0 m/s[/tex]

         The time is  [tex]t = 0.15s[/tex]

         The velocity at t is  [tex]v = 16 m/s[/tex]

  Generally average  angular acceleration is mathematically represented as

                [tex]\alpha = \frac{w_f - w_o}{t}[/tex]

        Where [tex]w_f[/tex] is the finial angular velocity which is mathematically evaluated as  

            [tex]w_f = \frac{v}{l}[/tex]

                  [tex]w_f = \frac{16}{0.85}[/tex]

                        [tex]= 18.823 rad/s[/tex]

 and [tex]w_o[/tex] is the initial angular velocity which is zero since initial linear velocity is zero

               So

                         [tex]\alpha = \frac{18.823 - 0}{0.15}[/tex]

                               [tex]\alpha =125.487 rad /s^2[/tex]