There are many answers to the question why is the earth bulged at the equator, but almost all of them involve centrifugal force. Since it's a fictious force, how to we explain this effect in an inertial frame. I guess there would be a similar answer to when we rotate a stone tied to a string, as we rotate it faster, the stone moves away from the axis of rotation. Please answer why does this happen, and don't involve the use of centrifugal force.

There are many answers to the question why is the Earth bulged at the equator, see e.g. here, but almost all of them involve centrifugal force. Since it's a fictitious force, how to we explain this effect in an inertial frame. I guess there would be a similar answer to when we rotate a stone tied to a string, as we rotate it faster, the stone moves away from the axis of rotation. Please answer why does this happen, and don't involve the use of centrifugal force.