So this is the problem:A wheel of radius of gyration k is placed on a belt moving with a speed v, which is maintained constant by means of an external agency. Assume that the axis of the wheel is fixed, so that the wheel is free to rotate about its axis perpendicular to its plane through the centre. We are required to find the energy supplied by the external agency till slipping ceases.
Now this might be due to two reasons, due to increase in kinetic energy of the wheel, and also the energy expended to move the belt at constant speed. My question is, are these two really the same, so that I need to count only one of these, or are these independent of each other. What I think is that the friction does some negative work on the system, and the exact negative of this work is the energy expended. So I need to sum the positive work on the wheel and the negative work on the belt, and the negative of this work will be the energy expended.Is this reasoning correct?