A crank drive mechanism is illustrated below. A uniform linkageBC of lengthL connects a flywheel of radiusr (rotating about fixed pointA) to a piston atC that slides back and forth in a hollow shaft. A variable torqueTis applied to the flywheel such that it rotates at a constant angular velocity. Show that for one full rotation of the flywheel, energy is conserved for the entire system; consisting of flywheel, linkage, and piston (assuming no friction).
Note that gravityg is acting downwards, as shown.
Even though energy is conserved for the system, why is it a good idea to make the components of the drive mechanism as light as possible (with the exception of the flywheel)?