Answer
$\alpha=1.3rad/s^2$
Work Step by Step
- The weight of the heavier block $W_1=(12kg)(9.8m/s^2)=117.6N$ produces a counterclockwise (positive) torque. The lever arm is $0.6m$
- The weight of the lighter block $W_2=(4kg)(9.8m/s^2)=39.2N$ produces a clockwise (negative) torque. The lever arm is $1.4m$
According to Newton's 2nd law of rotational motion, $$\sum\tau=I\alpha$$ $$(0.6m)W_1-(1.4m)W_2=I\alpha$$ $$I\alpha=15.68$$ $$\alpha=\frac{15.68}{12}=1.3rad/s^2$$
