Torque in a rotating wheel about a axis 
In the given situation there wheel is rotating about its own axis as well as about the axis PQ. Now my Query is that which torque of which force is responsible for the rotation of the wheel about axis PQ. I could not find any external torque on the rod plus wheel system which is in the vertically upward direction .Pls help me out in this. I hope my question is clear. If it is not please do watch the video the link of which I have attached.
https://www.youtube.com/watch?v=XPUuF_dECVI  (Start from 24:30 minutes)
 A: Interesting question. So first of all notice that there is a transient situation between the instant when the wheel is connected to the rope (with zero precession angular velocity) and the instant when the precession reaches the stationary angular velocity $\omega_{pr}=\tau/L_s$ (uniform circular motion of the center of mass around the axis).
We can't see this because the time interval between these instants is very small.
In this transient situation, the center of mass has an accelerated circular motion, produced by a centripetal force and a tangential force. After that, when the precession is stationary, the circular motion of the center of mass is uniform, with a centripetal force only.
Both these forces are vincular reactions provided by the rope and are applied to the point P. However these forces do not provide a torque with respect to the point P because they act exactly on that point.
Although the torque vanishes, the forces are still there and they are responsible for the circular motion of the center of mass.
A: This is the simple gyroscope situation. The torque that causes precession is the torque from gravity: r x Mg.  This torque produces a change in angular momentum in a direction into the page.  The wheel has an initial angular momentum Ls, and the torque adds the change in angular momentum to this initial value to produce the new angular momentum.  For Ls very large compared to the change in angular momentum, the wheel precesses around the PQ axis (counterclockwise viewed from above). A good basic physics text discusses this (e.g. Halliday and Resnick, Physics).  More advanced mechanics texts address details of the motion (e.g. nutation as well as precession using the Lagrangian for the motion, e.g. Symon, Mechanics).  Note: if the wheel is not rotating initially (no initial angular momentum) the angular momentum from the torque from gravity causes the wheel to "fall" .
