on every gram of our being, while proper-accelerations are usually caused by an external force. Introductory physics courses often treat gravity's downward (geometric) acceleration as due to a mass-proportional force. This, along with diligent avoidance of unaccelerated frames, allows them to treat proper and coordinate acceleration as the same thing. Even then if an object maintains a constant proper-acceleration from rest over an extended period in flat spacetime, observers in the rest frame will see the object's coordinate acceleration decrease as its coordinate velocity approaches lightspeed. The rate at which the object's proper-velocity goes up, nevertheless, remains constant. Thus the distinction between proper-acceleration and coordinate acceleration allows one to track the experience of accelerated travelers from various non-Newtonian perspectives. These perspectives include those of accelerated coordinate systems (like a carousel), of high speeds (where proper and coordinate times differ), and of curved spacetime (like that associated with gravity on Earth). Classical applications At low speeds in the inertial coordinate systems of Newtonian physics, proper acceleration simply equals the coordinate acceleration a=d2x/dt2. As reviewed above, however, it differs from coordinate acceleration if one chooses (against Newton's advice) to describe the world from the perspective of an accelerated coordinate system like a motor vehicle accelerating from rest, or a stone being spun around in a slingshot. If one chooses to recognize that gravity is caused by the curvature of spacetime (see below), proper acceleration differs from coordinate acceleration in a gravitational field. For example, an object subjected to physical or proper acceleration ao will be seen by observers in a coordinate system undergoing constant acceleration aframe to have coordinate acceleration: Thus if the object is accelerating with the frame, observers fixed to the frame will see no acceleration at all. Similarly, an object undergoing physical or proper acceleration ao will be seen by observers in a frame rotating with angular velocity to have coordinate acceleration: In the equation above, there are three geometric acceleration terms on the right-hand side. The first "centrifugal acceleration" term depends only on the radial position and not the velocity of our object, the second "Coriolis acceleration" term depends only on the object's velocity in the rotating frame but not its position, and the third "Euler acceleration" term depends only on position and the rate of change of the frame's angular velocity. In each of these cases, physical or proper acceleration differs from coordinate acceleration because the latter