So given a set of wheels with an axle if the centre of the axle hangs from a spring are you saying that the spring will stretch more if the wheels are not spinning?
Harry > >From: David Jonsson <[email protected]> >To: vortex-l <[email protected]> >Sent: Fri, December 10, 2010 9:25:07 PM >Subject: [Vo]:A rotating molecule on a rotating planet appears lighter than a >non rotating molecule > >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 > >
