In a laboratory centrifuge that uses sample tubes, the radial acceleration causes denser particles to settle to the bottom of the tube, while low-density substances rise to the top.
12.
Using the Schwarzschild basis, a frame field for the Schwarzschild metric, one can find that the radial acceleration required to hold a test mass stationary at a Schwarzschild coordinate of r is:
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By Newton's second law of motion, the magnitude of "'F "'equals the mass " m " of the particle times the magnitude of its radial acceleration
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Multiple editors including myself have tried walking David through the derivation, but he adopts some rather strange limitations to the derivation ( his vector triangle argument ) and uses very nonstandard terminology ( like what he calls radial acceleration ).
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Apart from the above physical arguments, of course, the derivation above, based upon application of the mathematical rules of differentiation, shows the radial acceleration does indeed consist of the two terms \ ddot r-r \ dot \ theta ^ 2.
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This root sum of squares of separate radial and tangential accelerations is only correct for circular motion; for general motion within a plane with polar coordinates ( r, \ theta ), the Coriolis term a _ c = 2 ( dr / dt ) ( d \ theta / dt ) should be added to a _ t, whereas radial acceleration then becomes a _ r =-v ^ 2 / r + d ^ 2 r / dt ^ 2.
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