Page 5113
|
8/21/04 |
Non-Inertial Frame |
A non-inertial frame of reference is any frame in which the law of inertia does
not apply. Examples would be accelerating frames, rotating frames, and flexing or
stretching frames (frames containing coordinate systems that vary with time).
In non-inertial frames of reference the coordinates of free bodies will change with time, not because the bodies physically move but because their coordinates change with time. Because the coordinates change, the positions of the objects appear to change, and free bodies appear to accelerate without cause in non-inertial systems.
The amount of acceleration depends upon how much the non-inertial system deviates from an inertial system. Therefore, a slowly accelerating or slowly rotating coordinate system will approximate an inertial frame while a rapidly accelerating or rapidly rotating system is obviously non-inertial.
For example, the earth is a non-inertial frame because it is rotating about its axis, revolving about the sun, and orbiting about our galaxy. But the rotation is so slow (once every 24 hours), the revolution so slow (once every 365 days), and the galactic orbit so slow (once every 225 million years) that the accelerations of these motions are completely negligible compared to other accelerations commonly encountered in everyday life.
As a result, most humans have developed the intuitive notion that the surface of the earth is an inertial frame and that they are perpetually living in an inertial frame. This notion is so strong that on the few occasions that they find themselves in a non-inertial frame they invent fictitious forces to account for the motion they observe.
They even give names to these fictitious forces. They say an inertial force thrusts them forward when a driver hits his brakes, a centrifugal force pushes them outward in a carnival ride, and a Coriolis force affects the weather patterns on the earth. Such fictitious forces can be distinguished from real forces by two characteristics: (1) real forces are always equal and opposite action/reaction pairs between two physical objects, and (2) fictitious forces are always proportional to the mass of the object on which they act.
Because gravity meets condition (1) classical physics treats gravity like a real force. But because gravity meets condition (2) general relativity treats gravity like a fictitious force. Therefore, gravity is different from all the other known forces of nature (electromagnetism, strong nuclear, and weak nuclear) in that it can be treated like a fictitious force and eliminated simply by switching from the earth frame to a freely falling frame.
Q1. Vibrating Drumhead.
Which of the following coordinate systems would best describe the surface of a
circular drumhead vibrating in its fundamental mode? (A)
Spherical polar coordinates (r, q, f). (B) Rectangular
Cartesian (x, y, z). (C) Cylindrical coordinates (r, f, z). (D) A
flexible coordinate system that moves with the surface. (E)
All of these coordinate systems are equally useful in describing the surface of
the drumhead.
Q2. Which are true? (A) In
non-inertial frames, objects will accelerate even when no physical forces act
on them. (B) NASA uses the term “micro gravity” rather than
“zero gravity” when referring to experiments performed inside
orbiting space stations because the effects of gravity there are often too
large to be completely ignored. (C) Magnetism is an example of a fictitious
force. (D) Two of these. (E) Three of these.
|