Classical Mechanics/Non-Inertial Reference Frames

From Wikibooks, open books for an open world
Jump to navigation Jump to search

It is very important to acknowledge how to construct equations inside of an inertial frame of reference. (As even the Earth is a non-inertial frame)

Consider an inertial reference frame S and a second reference frame S0 which is moving with respect to S with a velocity and accelerating with respect to S at a rate .

From the inertial reference frame (S) Newton's second law will hold and any object of mass m will be observed to have a force acting on it of where is measured from the origin of the frame S.

From the non-inertial frame (S0) we must relate the quantities using the Galilean transformation for a moving reference frame, so that the velocity of the mass in the new reference frame is . Using this fact we can differentiate ( ) and then substitute the force in the inertial frame ( ) to get an expression for the force measured by an observer in the non-inertial frame : .

The conclusion that we can reach is that we may continue to use Newton's laws in the non-inertial frame, so long as we add the additional "force" due to the motion of the frame, which is often called the inertial force :