A centrifuge with very light arms (neglect their mass) 10 cm long spins down samples of a colloidal mixture (one in each tube) at 3000 rpm. The arms are jointed at the top and swing out as the device spins up so that the bottom of the sample tubes exert a (normal) force on the samples that is always directed back along the arms. Find:
a) The equilibrium angle 
that the arms make with the stand
when the centrifuge is operating at full speed;
b) The effective centrifugal ``pseudogravity'' produced by the device,
expressed as a multiple of 
. This is why centrifuges work so well
to separate mixtures.