In Feynman's book, when he talks about the motion of a rapidly spinning top, he mentions:
"When we apply a Torque to a rapidly spinning top, the direction of the precessional motion is in the direction of the torque or at right angles to the forces producing the torque."
That is, if a top is only spinning, then after applying a Torque, it will start precessing. However, I'm confused as to how the direction of torque and the precessional motion, the same?
For simplicity let's say the spinning top is at a 45 degrees angle to the vertical.
The diagram shows that the precessing motion that sets in makes the spinning top sweep out a cone. That is, the center of mass of the spinning top goes around in a circle.
As the precessing motion commences the center of mass of the spinning top is moving in the direction that the torque vector is pointing. (The instantaneous direction of velocity of the center of mass is tangent to the circle of the precessing motion.)
As the precessing motion starts going the orientation of the spinning top changes, and the direction of the torque vector changes accordingly. From that point on the instantaneous direction of precessing motion is at all times in the direction of the torque vector.
To understand the onset of gyroscopic precession see my 2012 answer about the mechanics of gyroscopic precession.
