Answer:
[tex]\alpha = 6.431\,\frac{rad}{s^{2}}[/tex]
Explanation:
The pulley is modelled by the Newton's Laws, whose equation of equilibrium is:
[tex]\Sigma M = T \cdot R = \frac{1}{2}\cdot M \cdot R^{2}\cdot \alpha[/tex]
Given that tension is equal to the weight of the bucket, the angular acceleration experimented by the pulley is:
[tex]T = \frac{1}{2}\cdot M \cdot R \cdot \alpha[/tex]
[tex]m_{b}\cdot g = \frac{1}{2}\cdot M \cdot R \cdot \alpha[/tex]
[tex]\alpha = \frac{2\cdot m_{b}\cdot g}{M\cdot R}[/tex]
[tex]\alpha = \frac{2\cdot (1.53\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{(7.07\,kg)\cdot (0.66\,m)}[/tex]
[tex]\alpha = 6.431\,\frac{rad}{s^{2}}[/tex]
