Answer:
The angular velocity is  
Explanation:
From the question we are told that 
     The mass of the block is  
      The of the pulley is  
       The radius of the pulley is   
 
        The radius  of the cord around the pulley is  
        The distance of the block to the floor is  
          
From the question we are told that the moment of inertia of the pulley is 
           
 Substituting value  
          
          
Using the Newtons law we can express the force acting on the vertical axis as 
               
          =>  
Now when the pulley is rotated that  torque generated on the massless cord as a r result of the tension T and the radius of the cord around the pulley is mathematically represented as 
                   
      Here  is the angular acceleration
 is the angular acceleration 
            Here  is the torque which can be equivalent to
 is the torque which can be equivalent to
               
   Substituting this above 
              
      
Substituting for T 
          
Here  is the  linear acceleration which is mathematically represented as
 is the  linear acceleration which is mathematically represented as
            
     
      
     ![mgr = \alpha  [ I + mr^2]](https://tex.z-dn.net/?f=mgr%20%3D%20%5Calpha%20%20%5B%20I%20%2B%20mr%5E2%5D)
    making  the subject
 the subject 
            
          
    Substituting values 
             
              
Now substituting into the equation above to obtain the acceleration 
              
                 
This acceleration is 
and v is the linear velocity with is mathematically represented as 
          
Substituting this into the formula acceleration 
         
making t the subject 
          
substituting value
       
      
Now the linear velocity is 
        
        
The angular velocity is  
        
So 
        
         
Generally 1 radian is equal to  0.159155 rounds or turns 
         So  5.59 radian is  equal to x 
Now x is mathematically obtained as 
          
             
  Also 
       60  second =  1 minute 
So   1 second  = z       
 Now z is mathematically obtained as 
          
             z 
Therefore 
               
               