“free fall is any motion of a body where gravity is the only acceleration acting upon it.” -Wikipedia
Question 1 - If an object is falling freely, will it follow the Earth’s rotation too? Or will the earth rotate whilst the object falls in a straight line (in its own reference frame). Or more simply put, does it have centripetal acceleration?
Question 2 - Assuming that the earth IS spherical AND has uniform density. Weight of the same mass is different at the Pole and at the equator; thus, the gravitational field strength, $g$ is different at those two places. Are these different values of $g$ also the same as acceleration of a body falling freely at those different places?