In the early part of his lecture Laithwaite uses a Victorian
gyroscope to demonstrate gyroscopic precession. Precession
describes a change in the direction of the axis of a rotating object,
so in this case a change in the spin axis of the gyroscope.
Laithwaite hangs weights from a Victorian gyroscope in order
to demonstrate precession
Diagram of Victorian gyroscope
used by Laithwaite to demonstrate precession
The weights that Laithwaite hangs of the gyroscope are
m'g where m' is their total mass.
the weight is added to the gyroscope (with the rotor spinning)
gyroscopic precession occurs. This precession is in a direction
perpendicular to the direction that the weight force acts. The
precession that occurs is demonstrated in the animation on the left
which shows a view from above the gyroscope as it precesses (parts of
gyroscope such as the base are omitted for clarity)
The weight that is hung of the gyroscope (represented by a
cross on the diagram to the left) is offset from the center of mass of
the gyroscope and stand. It is this offset of forces which
Side view of gyroscope showing offset
It can be seen
to hanging the weight off the gyroscope all
the forces acted through the same point (the center of mass), there
was no precession in this case. From b) it can be
seen that all the forces no longer act through the same point and are
offset by a distance, d. A couple
is defined as a system of forces with a resultant moment but no
resultant force. Therefore b) is equivalent to a) with a moment, Q also
Side view of b) with
the offset of forces represented as a moment
can be seen that by
hanging a weight of the gyroscope in the
position shown a moment has been introduced into the system.
the rotor is defined as where C is a
constant given by the principle
of inertia about the k axis. From this formula it can be seen
the direction of the moment of momentum vector coincides with the
direction of spin of the rotor.
the information that
the offset force can be represented as a
couple and the direction of the moment of momentum vector is parallel
to the spin the precessing gyroscope can also be represented as
The gyroscope is
mounted on a stand and so the center of the rotor is a
fixed point therefore this can be simplified to
This result is key, the
moment of momentum vector, h
is changed a small amount in the direction of Q (the applied
direction of the couple and spin vectors can be
hand screw rule.
From this the direction of precession is obtained using the information
that the moment of momentum and so spin axis is changed in the
direction of the applied couple.
absence of the
weight precession did not occur this
due to the fact there was no applied couple Q and so no change in the
moment of momentum in other word the spin axis stayed fixed.
Toy gyroscopes provide a
demonstration of precession. In
this case it is not an applied weight which results in a couple but the
fact that center of mass of the gyroscope is not above the point of
contact and so the weight force and reaction force are offset.
The offset of
results in an applied couple, Q.
The point of the gyroscope that is in contact with the top of the
tower stays stationary, so here and
precession occurs about this point. The direction of
is dependent on the direction of spin of the rotor.
Toy gyroscopes are easy to
get hold of in
most toy shops, so this can be tested and the direction of spin varied
to see what happens to the direction of precession. The moment of
momentum vector,h will always move in the direction of the
Another motion nutation can also be observed during precession, thus is a steady state motion of the bodies k axis about the K axis with constant angle between them, it is observed as a fast wobbling motion