You have a weightless rod with a wheel attached to one end (weightless, frictionless) and a weight attached to the other. The weight is mounted on a short axle, and can rotate freely. With the wheel on the floor, the rod is held at 45 degrees to the horizontal and then released. Since the rod and wheel are weightless, the weight falls purely vertically while the wheel rolls across the floor, and we can work out the linear energy developed when the weight hits the floor from its height. The action is repeated, except this time the wheel is blocked. The weight falls in a curve, but because the starting and finishing heights are the same as in the first trial, the KE developed is the same. And being mounted on an axle, the weight doesn't rotate either, so the energy developed is purely linear, as in the previous trial, and must be the same. The paradox for me is that in the second case the weight has undergone a horizontal displacement, but has apparently used no energy to achieve it. What's the explanation for that?