[tex]\alpha = 35\:\text{rad/s}^2[/tex]
Explanation:
Newton's 2nd law, as applied to rotating objects, can be written as
[tex]\tau_{net} = I\alpha[/tex]
where I = moment of inertia
= [tex]\frac{1}{2}MR^2[/tex] for a disk
M = mass of disk/pulley
Since the hanging mass m is the only providing torque on the pulley, we can then write NSL as
[tex]\tau_{net} = (mg)R = \dfrac{1}{2}MR^2\alpha[/tex]
Solving for the angular acceleration [tex]\alpha[/tex], we get the expression
[tex]\alpha = \dfrac{2mg}{MR} = \dfrac{2(1.2\:\text{kg})(9.8\:\text{m/s}^2)}{(2.8\:\text{kg})(0.24\:\text{m})}[/tex]
[tex]\:\:\:\:\:\:\:= 35\:\text{rad/s}^2[/tex]
