video, a gyroscope on a large base precesses.
Laithwaite then moves the base forward till the gyroscope is hanging
off the top of a table. The gyroscope continues to precess.
pivot point marked in the above diagram is then clamped with the base
still hanging over the table. Counter weights are now required on the
back of the
base to ensure that it does not topple from the table. This is shown in
the image below.
The stand is
also placed with the gyroscope hanging underneath the table
with the pivot point unclamped as shown in the following picture.
videos it can be
seen that precession occurs as before and the stand does not topple off
Precession occurs with the pivot point unclamped.
following shows what happens when all the weight of the gyroscope is at
the pivot point. When the gyroscope is precessing the weight
essentially acts at the pivot point as the couple due to the weight of
the gyroscope is balanced by the change in moment of momentum
(precession) (see the following explanations).
the gyroscope is clamped so hanging out from
the table the couple due to its weight causes the stand to topple. When
the gyroscope is claimed in the other direction it can be seen that the
stand does not topple.
the pivot point unclamped precession still occurs even when the
stand is "upside down".
The assembly topples from the table when the
center of mass is no longer 'above' the table. A comparison between the
calculated center of mass of the assembly in each scenario and the
distance the plate is hanging off the table before it topples is given
in the table below (distances are quoted from right hand edge of
Calculated center of mass (mm)
Point toppling occurs in
expected the assembly topples when its center of mass is no longer
'above' the table top.
(1) Pivot point unclamped with
gyroscope precessing on stand hanging off table
gyroscope precesses about the pivot point (see here for an explanation of
why precession occurs), the following shows a diagram of the forces
acting in this demonstration.
this diagram assumes slow enough precession that the d'alembert force
is zero - including it does not effect the principles in the
is the offset of forces that causes precession.
The gyroscope is held up because the moment of its weight about the
support is balanced by the change in direction ofthe
moment of momentum, h.
Since the moment is of its weight is balanced by the change in
direction of h
this moment does not contribute towards toppling the stand. It can be
seen in the videos that the stand topples at the same point that it
topples when the weight of the gyroscope is at the pivot point, this is
expected and shows how the moment of the weight of the gyroscope about
the pivot point does not contribute to toppling the stand. The stand
topples at this point due to the fact that the center of mass of the
whole assembly is no longer on the table.
Pivot point clamped
As seen and
explained in video 6
precession doesn't occur when the pivot point is
clamped, as there is no net couple. When the gyroscope is clamped in
the following position the stand topples.
toppling is due to the pivot point being clamped meaning a moment can
be transmitted. The following shows a free body diagram of the clamped
stand in the position above.
The moment can
be seen to have the effect of contributing towards the toppling of the
the gyroscope is clamped with the rotor facing in towards the table
toppling occurs when the plate is hanging further off the table, this is because the moment here does not
contribute to the toppling of the stand but acts in the other
direction, as seen in the following free body diagram.
Pivot point unclamped with gyroscope precessing whilst hanging
underneath the table
the gyroscope is "hung under the table" and precesses as in this
demonstration the same principles apply as when the gyroscope is
on the table and precessing.