Noninertial Frames of Reference

Newton's Mechanics is valid in any inertial frame of reference. This will be upheld and even extended when we study Special Relativity.

Some convenient frames are non-inertial. The most important case for us is a coordinate system fixed on the earth. An earth fixed frame is potentially quite complex but it boils down to a rotating coordinate system.

The motion of the earth includes:

  1. rotation around an axis perpendicular to the equatorial plane.
  2. orbital motion around the sun
  3. orbital motion with the moon
  4. the sun's motion in the galaxy
  5. the motion of the galaxy in the cluster of galaxies and the rest of the universe.
While all of these involve acceleration, 2-5 are objects in free fall in a gravitational field. The force of external gravity on an object on the earth is canceled by the acceleration of the earth due to that force. Just like an astronaut inside a satellite in orbit around the earth feels no force of gravity or fictitious force due to the acceleration of the satellite. They just cancel. (But they only cancel at the center of the earth, leaving tidal forces elsewhere.) In fact in general relativity, we understand that acceleration and gravity are the same thing and there are no forces on objects in free fall.

This is not true for the rotation of the earth.

Jim Branson 2012-10-21