Determining the radius/length of an IMU on a rotating stick
The problem would be simpler if the arm were pivoted some distance above the ground so that it could rotate continuously at a steady speed.

In that case, you could determine the rotational rate via the gyro sensor, or by timing the changing presence of gravity in the acceleration reading.

You could then measure the centripetal acceleration with your accelerometer, and with that and the angular rate calculate the radius.

In theory, you could make a similar analysis even when the rotation has to start from a standstill and stop again before hitting the ground on the other side as your drawing seems to show - however, it will be more complicated and more sensitive to error in determining the instantaneous angular rate (probably now from the gyro exclusively, unless your mentioned ability to measure the angle refers to some sort of encoder at the motor rather than being limited to the IMU).

You will not be able to deduce anything from static measurements (at least for any practical arm length).  Further, the error of your measurements will probably be lower the faster you can rotate, up to the point where the centripetal acceleration is mid-range on the accelerometer - that's part of why a system that could rotate continuously would be easier to measure than the limited range one you have drawn.