A B-24's wheels and tires were modified with vanes attached that would spin the wheels up to the same speed of the aircraft. Sounded good and it was a simple idea with very little weight penalty.
One problem though. When the wheels spun up to the speed of the aircraft, the gyroscopic forces caused by the spinning wheels and tires was so strong, the aircraft could not turn.
The project was dropped.
I used to fly B-24's. Specifically, a variant of them which used the same airframe, save for the vertical and horizontal stab. Rest assured, there is nothing about wheels spinning while the airplane is airborne which prevents turning, and the gyroscopic forces aren't that great. I've stopped the wheels before and during retraction, and simply let them retract while spinning, while maneuvering, and it has no appreciable effect on the control of the airplane.
Standard procedure was to apply gentle braking shortly after takeoff, to stop tire rotation; not because spinning wheels made aircraft control difficult, but because the other method of stopping them was rubber strips in the gear well, and it reduced vibration. If the gear was retracted without stopping the spinning, it would be stopped in the well. A number of modern aircraft use a similar method, or use backpressure in the brake system to stop the wheels during retraction.
it also got me thinking about how much gyroscopic force must be created by the gear at this point of take-off,and what effect if any it would have on the aircraft..
Nothing of significance.
By the same token, braking the wheels once in flight would produce a net pitching moment. Would that be significant?
No. It produces no pitching moment.
I expect this has been asked before, but why are aircraft not fitted with a motor or an aerodynamic device to spin the wheels up to speed before touch-down? I would have thought the savings in tyre wear and general wear and tear would be considerable, but the idea is so obvious that there must be a good reason why not.
Weight and complexity. There's no reason to spin the wheels up. In fact, spin-up logic is used to arm anti-skid systems, and to perform certain functions during landing with systems such as autospoilers, autobrakes, etc.
Most large airplane operations (airlines, etc) use re-tread tires; these are very common. When wheel wear becomes significant, it's not the loss of rubber that's the issue (as in a tire getting thinner), but balance. Tires are resurfaced or "retreaded." Rather than add cost and complexity to an airplane by spinning up wheels, it's less expensive, less complicated, and safer to simply retread the tires.