Which is more efficient: a larger wheel or a smaller wheel? I'm designing a 2-wheeled cart that I plan to rig to a donkey for hauling work around a farm. I'm wondering if there are mechanical advantages to using smaller wheels (like 40 cm diameter) vs. using larger wheels (like 50 cm diameter). 
 A: I agree with @ja72 answer, except for what seems to me a minor slip
(the kind I do all too often). I think he meant more energy to start
or stop rather than more force, the same force for a longer time, or more force for the
same acceleration.
Also the energy increase is only due to the fact that a large wheel is
likely to have a greater mass. If the mass of the wheels is the same,
distributed homothetically for the two sizes of wheels, then the
innertia of the larger wheel does increase but this has no effect
since the wheel angular speed will slow proportionally to its size for a given cart speed. The two changes cancel out for kinetic energy.
A: Larger are better because they can roll over stuff better (like gravel or sticks), but have more inertia and so require more force to start or stop.
Also the larger wheel requires less friction to roll because the ratio of wheel diameter to axle diameter is larger.
There are some trade-offs as you try to make the wheels as thin as possible to reduce weight, they become unstable and more difficult to keep upright unless you have really tight clearances in the bearings. A wider wheel is somewhat self righting as the wider footprint provides for a restoring moment.
A: A larger wheel.(let's consider the formula for work. Work= force x distance) As an example  If you put the same amount of work, (24j)  into the large wheel ( with the circumference of 6m) and the smaller wheel ( circumference of 3m), you see that the force required the formula would be larger for the smaller, as the Work= 24J meaning that 24/ by the radius of the smaller circle, (3) would have the be 8. Whilst the larger circle would be 24/6 ( the circumference of the larger circle) which would be 4. Meaning the larger circle in this equation would be 2x easier to turn.
