MotoGP motorcycles lift front wheel while exiting curve I've seen multiple times now in MotoGP that motorcycles were leaving a curve, and because of the acceleration the front wheel is slightly leaving the ground. But at the same time they were still leaning to the inside of the curve, just following the curve to the end and then going straight again.
Now I understand why the can lift the front wheel. But what I don't get is why they can still finish the curve on one wheel, instead of just going straight and leaving the track. I thought the front wheel is supposed to use its traction on the surface of the ground to lead the motorcycle around the curve, but they keep going around the curve while the front wheel is in the air.
Which force makes the motorcycle do a curve while the front wheel is not touching the ground?
I'm not sure if my explanation was understandable, here are some pictures of what I mean. They still lean into the curve and follow the curve while already lifting the front wheel:
http://50to70.com/wp-content/uploads/2012/07/jorge-lorenzo-motogp-2012-mugello-test.jpg
http://farm3.static.flickr.com/2224/2331275819_ccbe52129f.jpg
 A: It is an interesting question and I know exactly what you mean. I often look at the likes of Stoner performing what you describe and think "wow!". Right, for the answer...
Although the front wheel of any bicycle plays a key role in providing stability, it is not required for cornering. The ability to change direction is provided by a centripetal force, which is usually provided by both wheels of the motorcycle. The front wheel in this case providing the stability to the bike via the 'mechanical trail' (see the aside below). However, if the front wheel is off the ground, this does not mean that the centripetal force required to corner cannot be achieved (although the rider has to be much more skilful by using one wheel without the stability provided by the front wheel's mechanical trail). Note, in the case of a 230-260BHP MotoGP bike, cornering at high speed, having one wheel off the ground does not mean that the act of cornering is too-fine-a balancing act, the rapidly rotating wheels in this case will provide a 'large' amount gyroscopic torque. You will often see riders turning the front wheel in the cases you mention. 

This acts to allows the rider to change the bikes trajectory, and pivot slightly about the rear wheel's point of contact and provide some lateral stability.

Aside: An interesting thing about the use of the front wheel to steer a motorcycle (or any bicycle for that matter) is 'mechanical trail' or 'caster'. This quantity is one thing that I was not aware of until I designed and made my own downhill racing bike many years ago. Mechanical trail is the perpendicular distance between the steering axis and the point of contact between the front wheel and the ground. It may also be referred to as 'normal trail'. This quantity is what determines how a bicycle handles when steering. See the picture below 

If the trail is positive (trail shown by the green arrows), the bike will be stable. The more trail, the "heavier" the steering. If this distance is (too) negative, you cannot steer you bike (try turning the handle bars of your push bike the wrong way around [we have all done it as kids but I don't recommend it!]. 
For me, the reasons for trail playing such a key role in the steering stability of a bike is (very loosely) 'causality'. The trail or 'lead' allows the rider to adjust the lateral force on the front tyre as required before the point of contact of the tyre travels the trail-distance. This is a poor, on-the-fly explanation of trail and why it works the way it does and I would be interested to hear some of the other guy’s thoughts on this... but that is another question entirely!
I hope this helps.
A: I've seen multiple times now in MotoGP that motorcycles were leaving a curve, and because of the acceleration the front wheel is slightly leaving the ground. But at the same time they were still leaning to the inside of the curve, just following the curve to the end and then going straight again. 
Part of the story, no doubt, is the effect that is called 'camber steering'. Once the motorcycle is leaning the contact point of the rear tire on the road is somewhat to the side of the tire. The tire is rounded, so when the motorcycle leans over what is on the road is effectively a cone-shape. And a cone does not roll in a straight line.
Also, when leaning over the contact point with the road follows a circle with a larger radius than the overall center of mass. That too will tend to turn the motorcycle in the direction of lean.
Thirdly, it may well be that the driver is allowing the rear tire to drift. I've seen that as a cornering technique. You'd think controlled drift of a motorcycle is undoable, but top racers are in fact capable of such a feat. 



Of course, the above considerations raise the question: how can the motorcycle racer straighten out again?
To straighten out the contact point of the rear tire with the road must be brought back underneath the center of mass. 
For instance, let's assume the racer is using controlled drift. I think when the racer eases up a fraction on the acceleration the rear tire has more of the needed grip, and the rear tire will move underneath the center of mass.
If controlled drift is not part of the story then I don't know how the racers do it. Still, the only thing that the racer can control directly is the power output of the engine. So in any case I think the racer is working the acceleration to straighten out again. 
A: When the majority of the turn has completed the racer cranks up the throttle, allowing the anti-wheelie control and stability control to do their job.  They are drifting outward.  I believe the reason is to on a fully open throttle, the slippage allowing the engine to spin at higher RPM's making more horsepower.  At some point they run out of headroom and either hit the rev limiter or do an upshift, that's when the front comes down.
