To solve this problem it is only necessary to apply the kinematic equations of angular motion description, for this purpose we know by definition that,
[tex]\theta = \frac{1}{2}\alpha t^2 +\omega_0 t + \theta_0[/tex]
Where,
[tex]\theta =[/tex] Angular Displacement
[tex]\alpha =[/tex]Angular Acceleration
[tex]\omega_0 =[/tex] Angular velocity
[tex]\theta_0 =[/tex]Initial angular displacement
For this case we have neither angular velocity nor initial angular displacement, then
[tex]\theta = \frac{1}{2}\alpha t^2[/tex]
Re-arrange for [tex]\alpha,[/tex]
[tex]\alpha = \frac{2\theta}{t^2}[/tex]
Replacing our values,
[tex]\alpha = \frac{2(40rev*\frac{2\pi rad}{1rev})}{60^2}[/tex]
[tex]\alpha = 0.139rad/s[/tex]
Therefore the ANgular acceleration of the mass is [tex]0.139rad/s^2[/tex]
