A disk of radius 25.0cm turns about an axis through the center. The pull on the string produces a linear acceleration a(t)=At on the ball The disk starts from rest and after 3 seconds, linear a(3)=1.80m/s2. Find A and then write an expression for the angular acceleration α(t).

The value for  A  is A= 0.6

The angular acceleration is  

Explanation:

From the question we are told that  

    The radius of the disk is  

     The linear acceleration is  

     At time  

Generally angular acceleration is  mathematically represented as  

Now  at t = 3 seconds  

         a(3) =  A *  3

=>      1.80 =  A  *  3  

=.>       A =  0.6

So  therefore

             a(t) =  0.6 t  

Now  substituting this into formula for angular acceleration

substituting for  r  

carla slowed down in the beginning of her trip, stopped, and then sped up