Finding angular acceleration from linear acceleration
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As you stated, the angular acceleration, tangential linear acceleration and distance between the reference point and the object are related using the following formula:
a⃗ =α⃗ ×r⃗ a→=α→×r→
r⃗ r→ is merely the displacement vector between your choice of reference point and the object. The object needn't necessarily move in a circle for the formula to work.
The choice of reference point is arbitrary; you can choose any point. We often use the centre of mass or the centre of rotation as it simplifies the math but there is no rule which states that you should do your calculations about that point only
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