A crank drive mechanism is illustrated below. A uniform linkage BC of length L connects a flywheel of radius r (rotating about fixed point A) to a piston at C that slides back and forth in a hollow shaft. A variable torque T is 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 gravity g 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)?