|Newton's equations describe and predict the way an object moves: but moves with regard to what?|
To derive the motion of a penny dropped inside an airliner moving at 600 miles/hr (about 1000 km/hr)--should we calculate it with respect to the interior of the airliner, or with respect to the ground? Or does it make no difference what the choice is? In that case it would be best to calculate the motion with respect to the airliner, a much easier job.
And if a similar penny is let go inside an orbiting spaceship--should its motion be calculated relative to the interior of the spaceship, or relative to the Earth outside? Or perhaps, relative to the Sun, around which the Earth moves at much greater speed? Or relative to the galaxy, inside which the solar system has its own motion?
Each such choice is known as a frame of reference. Some possible frames are
-- the surface of the Earth, or
-- the distant stars with respect to which the Earth rotates and moves.
Choosing the Frame of ReferenceObervations suggest that among all such choices, the frame of the stars (or of "the distant universe") is the proper one for Newton's equations.
However, this is not always the most convenient frame: for someone sitting in a moving airliner, in an orbiting spaceship or upon the rotating Earth, it is much easier to observe the way an object moves relative to its immediate surroundings than to figure out its motion relative to the distant universe! It is therefore often much preferable to derive the corrections which must be applied to the laws of physics in the local frame of reference, and then by taking those corrections into account, calculate the local motion.
Two rather typical cases are examined, here and in the next section. In those cases, relative to the rest of the universe, the local frame--
(2) Rotates at a constant rate around a fixed point.
(1) Constant velocity in a straight lineSuppose we sit in an airliner (or in a train, or on a ship) that moves with a velocity v0 , constant in direction and magnitude ("uniform motion"). Strictly speaking, this constancy should be with respect to the "absolute frame" of the distant universe. Here, however, we shall only assume constancy relative to the surface of the Earth, and later show that this gives a pretty good approximation to the "absolute frame."
How do observations differ in the two frames--the airliner cabin and the Earth? Very simply: any velocity v measured inside the airliner corresponds to a velocity
is the rate at which v changes.
--the acceleration a' with respect to the ground
is the rate at which v' changes.
And because the accelerations are the same, so are the forces:
In the frame of the Earth F' = ma'
All laws of mechanics remain the same in
Next Stop: #22a Airplane Flight
Author and curator: David P. Stern
Last updated6 March 1999