How to pick a stepper motor
I've asked about the exact geometry of the system and have not received an answer. So I'll make some assumptions. I'll assume the plank is 2 feet by 4 feet by 3/4 inch plywood. 1/2 inch strikes me as being pretty weak. I assume that the stepper is attached at the midpoint of one 4 foot edge, and the axis of rotation is parallel to the 2 foot edges. This plank will consist of 1/4 sheet of a standard 4 x 8 sheet of plywood. Assuming 40 lbs per sheet the piece will weigh 10 pounds.

As mkeith has pointed out, minimum rotation time for a given motor torque and rotation of 90 degrees corresponds to acceleration for .25 seconds followed by deceleration for .25 seconds, with the rotation reaching 45 degrees at the end of the acceleration. In other words, $$\theta = \frac{\alpha t^2}{2} $$ and $$\alpha = \frac{T}{I} $$ where T is the motor torque. For a thin rectangular slab with radius r from the axis, $$I = \frac{m r^2}{3} $$ Combining these, $$T = \frac{2\theta I}{t^2} = \frac{2\theta mr^2}{3 t^2} = \frac{2\times (\frac{\pi}{4}\times 10\times 2^2 )}{3\times (.25)^2} = 134 \text{ ft-lb} = 182\text{ Nm}$$

I'm not sure this is possible, see here, for instance for a 38 Nm motor but the motor will be large (NEMA 66 for the example) and require a lot of current. The example motor weighs 53 lb and draws 10 or 20 amps depending on model.

So I'd recommend a motor with some sort of gear reduction.