I don't know about this explanation. Why should a force be applied 90
degrees later?


To attampt to answer the question I think you're asking, consider a rotating
object (such as a propeller). Imagine it rotating in front of you, clockwise
from your point of view, and in the vertical plane. When the tip of one of the
blades is at the top of the disk, it is travelling to the right.

Note that (given the hub in front of you), having the tip travelling to the
right defines the disk - that is, there is only one orientation in which the
prop can be spinning which puts the hub in front of you, and the tip of the
prop at the top of the disk travelling (purely) to the right.

Now, apply an impulse, away from you, to the tip of the prop blade just as it
passes the top of the arc. (for symmetry, apply the same impulse, TOWARDS
you, to the other blade which is now at the bottom of the prop arc). This is
the same as applying a torque DOWNWARD (trying to point the nose down, if you
are envisioning yourself in the cockpit).

The tip of the prop blade at the top of the arc is now travelling not PURELY to
the right, but rather, to the right and away from you. The one at the bottom
is travelling to the left, and also towards you (due to the impulse you gave
it). Assuming the blades remain connected to the hub (!) the one at the top
will swing out as it goes to the right, and then swing back as it reaches the
bottom (where it will be travelling to the left and towards you)... while the
one at the bottom will swing towards you as it moves to the left, swinging
around and back away from you as it reaches the top.

The prop disk has rotated to the left, from your point of view, though you gave
it an impulse "down".

The key here is that when you push on a gyro, you are attempting to change the
VELOCITY of the rotating parts (making them move in a different direction).
This causes a change in POSITION which you can see or feel.

Mathematically, velocity isn't the same as position, it is the derivative (rate
of change) of position. For sine waves (and circular motion), derivatives are
90 degrees out of phase with each other (the deriviative of the sine is the
cosine, which is also the sine of the angle 90 degrees away from the original
angle)

Jose


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