Hi all, Some time ago I watched this video about an intra-terrestrial elevator. It is about a theoretical elevator that goes through the Earth that no matter where it starts and ends on the surface, it takes 42 minutes of travel time. Naturally, I wanted to see if I could work out the equation that showed this and I managed to do so. You can see my solution here. However in it I assumed that the Earth is not rotating and I would like to know what would happen if I did not make that assumption I do believe that if the Earth is rotating, it will affect the speed of the elevator because as it travels it changes it's radius and so will have to change its tangential speed, since the angular velocity matches that of the Earth (the walls of the shaft will prevent it going faster/slower than the Earth). Now there are two cases: If the path of the elevator is straight through the core, the changes in the tangential speed are irrelevant, because this speed is always perpendicular to the path of motion. So it will take 42 minutes no matter what. If the path of the elevator is at some weird angle such that a component of the tangential speed is parallel to it, then I am not sure what would happen. I am thinking that I can split the net force into two components. One would be the centrifugal force, which keeps the elevator going in circle. This force does not change the speed of the elevator, since it's perpendicular to the path of motion. The second force would be the force that does change the speed, which is due to the changes in potential energy as the elevator changes the radius. Since I am only using these changes in potential energy for my solutions, then the equations for the speed should be right and so the equation for the time should be right. However it somehow seems that some of my reasoning applies only to inertial frames, but rotation is non-inertial... What do you think, would it take 42 minutes to use the elevator even if the Earth was rotating?