Gyroscope hanging over the top of a table
In this 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.
(1)
The 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.
(2)
The stand is also placed with the gyroscope hanging underneath the table with the pivot point unclamped as shown in the following picture.
(3)
Repetition of demonstration
(1) Precession occurs with the pivot point unclamped.The 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).
(2)Pivot point clamped.
When 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.
(3)
With the pivot point unclamped precession still occurs even when the stand is "upside down".
Explanation of motion
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 plate).| Scenario | Calculated center of mass (mm) | Point toppling occurs in practice (mm) |
| Precessing | 121 | 120-130 |
| Clamped facing out | 99 | 90-100 |
| Clamped facing in | 142 | 140-150 |
| Upright | 121 | 120-130 |
| Precessing under table | 121 | 120-130 |
As 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
The 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.
(note this diagram assumes slow enough precession that the d'alembert force is zero - including it does not effect the principles in the explanation)
It 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 of the 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.
(2) 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.
The 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 stand.
When 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.
(3) Pivot point unclamped with gyroscope precessing whilst hanging underneath the table
When the gyroscope is "hung under the table" and precesses as in this demonstration the same principles apply as when the gyroscope is sitting on the table and precessing.