Generally, our center of rotation is not at the origin. We can simply fix our equation to handle this case. We introduce the center of rotation, o.

This equation states that the total velocity at a point is the sum of the point's angular velocity and the velocity seen at the center of rotation. The total acceleration is given by differentiating once more.

Often, you will see the angular velocity vector defined as:

What's going on with that third term in the total acceleration expression?