|Jun28-12, 09:27 PM||#1|
Something I've never understood about non-inertial reference frames
Basically: I jump forwards, exerting an amount of energy enough to push me forward with some velocity.
But in my reference frame, I exert the same force, except the entire universe moves backwards with that same velocity, where did that energy come from?
I sort of know this has to do with fictitious forces, but I'm not sure how.
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|Jun28-12, 10:21 PM||#2|
I'm not sure about your jumping example. For me one way of looking at non-inertial reference frames is kind of like this (but I'm open to critiques from people):
Say you're on bus. You and everyone else in the bus, (and the bus itself), are happily sitting around stationary, while the entire rest of the world streams backwards past you at a constant speed. You notice that the driver puts his foot down, depressing a pedal on the floor. At this point, you feel a force throwing you forward in your seat. You look out the window and notice that, although the outside world is still streaming backwards past you, it is not doing so as quickly as it was before. In fact its rearward motion is slowing. If its backwards speed decreased, then it must have been experiencing a forward acceleration. What provided this forward acceleration to the outside world? Why, it was the very same forwards force that just suddenly appeared and threw you forward in your seat!
Where did this magical "sideways gravity" come from? Who knows? But you must take it into consideration in order for Newton's laws to still appear valid to you, and it certainly felt real enough to you...
|Jun28-12, 11:23 PM||#3|
Yes, it's the fictitious forces. In non-inertial reference frames, there generally appear bizarre forces. For example, in rotating reference frames, everything becomes subject to the centrifugal and Coriolis forces in addition to the familiar forces of gravity, electromagnetism, etc. These new forces are strange beasts that, like gravity, are proportional to mass, but depend on the position and velocity of the objects they act on in a way very different from gravity. For example the centrifugal force is like a gravitational field that points radially *outward* from the origin and has a magnitude proportional to your distance from the origin. Similarly in a linearly accelerating reference frame there appears a force that looks like a uniform gravitational field permeating the universe, which starts accelerating everything else in the universe backwards.
Inertial reference frames can be *defined* to be the reference frames free of these strange forces, in which the laws of mechanics take their simplest form.
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