Hi
I was calculating and found a strange thing. It seems like a rotating
molecule is less effected by gravity compared to a non rotating molecule.
Imagine a diatomic molecule at the equator of a rotating planet. The
molecules has its axis of rotation parallel to the planets axis. It seems to
me that the centrifugal force on the molecule is different when the molecule
rotates and when it is not rotating.
Speed of surface of the rotating planet = v
Radius of planet = r
Speed of the atoms in the rotating molecule = u
Mass of molecule = m ,(m/2 for each atom)
In the non rotating case the centrifugal force on the gas molecule becomes:
f = m v^2 / r
If the molecule rotates the centrifugal force is different on the two atoms
it consists of. Lets take the case when the molecule is vertical like this
O <---- rotation of upper atom
I
O ----> rotation of lower atom
<---- rotation of planet
----------Planet surface-------
The centrifugal force on the upper atom becomes
fu = m / 2 * (v+u)^2 / r
and on the lower
fl = m / 2 * (v-u)^2 / r
adding the forces together to find the net effect gives
f = fu + fl = m / 2 * (v+u)^2 / r + m / 2 * (v-u)^2 / r =
= m / 2r * ((v+u)^2+(v-u)^2) =
= m / 2r * (v^2+2uv+u^2+v^2-2uv+u^2) =
= m / r * (v^2+u^2)
The effect is of course smaller at other positions of the molecule and the
mean value over an entire revolution would be somewhat lower but still
higher than the case when the molecule is not rotating.
It seems that the centrifugal force on the molecule is higher when it
rotates. Since the centrifugal force is opposed to gravity it means that the
rotating molecule would be less affected by gravity than the rotating one.
Can this really be the case? It has to apply to all rotating matter and not
only molecules as for example a rotating planet around a star.
Have I done something wrong?
David
David Jonsson, Sweden, phone callto:+46703000370
