I realize there is another question on the centripetal force involved in a gyroscope's motion, but I found the answer to not be very complete.
With respect to a gyroscope attached to a vertical spring - I understand that precession of a spinning gyroscope is caused due to a torque (due to weight of the wheel and tension in the string which act as a couple) which changes the direction of angular momentum of the wheel about its central axis. However, in a question I solved, the string was said to be at an angle to the vertical, such that the horizontal component of tension provided the centripetal force necessary for the circular motion. I am a bit confused about this - centripetal force in the case of a ball attached to a string rotating in a horizontal circle acts so as to maintain the circular motion and ensure the ball does not fly off in a straight line path with its linear velocity at that instant.
However, in the gyroscope case, doesn't the torque constantly keep changing the axis of rotation such that the gyroscope moves in a horizontal circle? It seems like the torque is what keeps the wheel moving in a horizontal circle by shifting the spinning axis in a horizontal plane, so why is there an extra centripetal force needed to be provided by a component of tension?