Actually I need to rotate the beam (pivoted at centre) with constant angular velocity using the priciple of mass imbalance. Could anyone suggest what would be rate of decrease of mass in one pan (while the weight in other pan is kept constant) to achieve uniform velocity rotation? How should i proceed?
To keep the balance rotating with uniform angular velocity, you must ensure that gravity (being the only force) must not do any work on any part of the system and the system as a whole. The way to do this is to keep the center of mass of the system always at the pivot throughout the motion so that torque due the balance's own weight is zero always. That is, if you are loading mass onto the pans, they better be equally loaded throughout the motion. Otherwise, if the center of mass is off-center at any instant (one pan is more loaded than the other),torque would act and the angular velocity would change at that instant itself. Thus not maintaining 'constant' angular velocity.