The heavy torque is not a constant torque, M= 1/2mglsinθ, and the work done by the heavy torque can be obtained by integrating θ from 90 degrees to 30 degrees.

On the right side of the equation is the kinetic energy change e =1/2j ω 2 =1/2 * (1/3ml2) ω 2.

The two sides are equal to find the angular velocity.

This gravity is a constant force. There is a ready-made constant force, so you don't have to do work with torque. This is not looking for abuse.