I can remember when i first started flying i was surprised to see the wheels stop spinning shortly after takeoff. I had excected them to keep spinning all the way through the flight as surely the wind blowing on them would make them spin (assuming fixed gear here guys).
Then, later when thinking about it i guessed on a couple of reasons as to why they dont:
1) A tyre (and wheel) is circular in shape (we hope!), so any wind as a result of your speed that 'hits' the wheel will hit all the forward parts with equal pressure. ie; the pressure on the wheel on an angle 45 deg up and down from the centre (like the equator on earth) will be the same. With no differential in the pressure there is no offset force to start the wheel spinning.
2) This one is probably to a MUCH lesser extent. The mass of the wheel is too great for the given speed.
On a side note here, I know some flying schools teach their students to gently press the brake pedals after takeoff to stop the wheels spinning earlier and thereby stopping any vibration through the aircraft. Most of the guys I know used to do that until we had something happen a while ago that we (the CP, engineers and pilots) think happened because of the above procedure. On landing one of our guys had a tyre come off the rim of the wheel, no great harm done but it was a nasty shock to the guy say the least. What they found on inspection of the tyre was that the valve on tyre (where you put the air in

proper lingo escapes me) had been broken. The cause, they believe was that as you brake after takeoff to stop the wheel rotating you are doing just that, stopping the wheel rotating but because of momentum the tyre actually 'pulls' ahead of the wheel minutely (the amount of movement dependant on the pressure of braking) and it was this tyre 'slip' on the wheel that had caused the valve to be disloged. The result is obviously the air escaping and a flat tyre.
Any thoughts on the above guys...
Twin