Why do motorcycles front wheels lift of the ground when accelerating quickly When motorcycles accelerate quickly they do a wheelie. Where is the torque provided to lift the motorcycle?
 A: Just like the force to accelerate the vehicle forward comes from the friction with the road, the torque on the vehicle comes from the same road friction.
Draw a free-body diagram with motorcycle.  As it begins to accelerate, the only external forces are gravity (with a torque about the rear axle in one direction), and friction (with a torque in the opposite direction).
If the torque from friction exceeds the torque from gravity, the front will lift.  As the vehicle starts moving, there is an additional pseudo-torque from the acceleration of the rear axle.

I thought the torque from friction would just be trying to rotate the back wheel not the entire bike.

In a sense, this is correct.  If the rear wheel were free to spin, then any torque from the road would only lead to an acceleration of the wheel itself.  But the torque from the engine opposes that.
We know that since the engine is driving the acceleration, it must be strong enough to oppose the road torque.  So this is a valid assumption.  If you didn't want to make that assumption, then you'd instead solve several simultaneous equations:
Torque from the engine and torque from the road on rotational acceleration of the rear wheel, torque from gravity, acceleration, and the road on the rotation of the entire vehicle, and assuming no slip from the tire, then the speed of the vehicle and rotation of the rear wheel must be identical.
A: It is due to the conservation of angular momentum. As soon as the motorcycle is accelerated, there's a rotation of the rear wheels, associated with it will be an angular momentum. So, one is introducing an angular momentum into the system. As there was no angular momentum before accelerating, the net angular momentum should also be zero after accelerating.
Therefore, to conserve the angular momentum, there will be rotation in the reverse direction about the axis of the rear wheel. The rotation of wheels is in the anti-clockwise direction as the bike moves ahead. So, there will be a rotation in a clockwise direction i.e. front wheel lifting up.
Hope this helps!
