I'll assume the plane containing the rim of the bicycle wheel is perpendicular to the bar you are holding.
One other thing that is important here is the change in the angle of the bar (you specify a distance, five inches, which is also important, in that raising the wheel five inches means you have to lift the wheel against the opposing force of gravity. Energy has to be expended to lift the wheel five inches whether the wheel is spinning or not).
What is different with the spinning wheel is the amount of torque you have to exert in order to change its direction. Torque is different from force, as we explain here
, and is measured in different units (pound-feet, or Newton-meters in English or MKS units, while forces are in pounds or Newtons, respectively).
The spinning wheel has angular momentum pointing along the axis of the wheel. To change the magnitude or direction of this angular momentum, a torque must be applied. If you are applying this torque with your hand, then it is easiest to push in one direction with the fingers on one side of your hand and push in the opposite direction with your thumb (a twisting motion). If you use two hands on the bar you can get quite a lot of torque using very little force, by spreading your hands far apart on the bar.
The other funny thing about torque and angular momentum is its geometry. Torque also has a direction, like angular momentum, but it is perpendicular to the force that is applied and also perpendicular to the distance through which it is applied. Thus pushing horizontally forwards with one hand and horizontally backwards with your other on the bar creates a torque pointing up (or down, depending on which hand is pushing forwards and which backwards). If you want to raise the angle of the bar relative to the horizontal direction, you have to change the angular momentum of the bicycle wheel, which initially points horizontally. Pushing forwards and backwards on the bar with two hands (or the fingers of one hand) will make the wheel tip up or down (also depending on which way the wheel is spinning) as you desire.
The torque applied is the rate of change of angular momentum. If you are not in a hurry, you can apply a small torque in the appropriate direction and the wheel on the bar will slowly change angle, and if you take long enough, you can get it to move to the angle you like. This motion is called "precession".
One thing you might want to be careful about is making sure that the torque needed to balance the weight of the wheel at the far end of the bar is supplied in the same way when the wheel is spinning as when it is not. This torque is needed to keep the bar from turning under the weight of the wheel and is perpendicular to the torque discussed above. Applying too much or not enough torque to hold the wheel up will cause the spinning wheel and the bar to precess in a horozontal plane (not what you wanted, but fun anyway -- you wanted to raise the angle of the bar).
(published on 10/22/2007)