This has to do with the motion of a board rocking on a circular pole. What made it so complicated is as the board rocks, the point of contact changes and that changes the moment of inertia for the rocking board as well as net torque. Variables are as follows.

angle between the board and horizontal (I'm using clockwise as positive, not that it matters)

radius of pole

accelerational constant of gravity

length of the board

angular acceleration

Once I divided the equation for torque by the moment of inertia the mass canceled out, leaving me with this equation.

From there eliminating the constants as best I could gave me what I put in my first post.