Whilst Professor of Electrical Engineering at Imperial College, London, Laithwaite was invited to give a Royal Institution lecture. He chose to demonstrate his observations on gyroscopic force, coming to a series of false conclusions on gyroscopic motion. As a result proceedings of the lecture were never published.
The videos of the 1974 lecture can be viewed at http://www.gyroscopes.org/
The demonstrations in Laithwaite's videos have each been repeated and the observed motion explained using Newtonian Mechanics. The repeated experiments and explanations of the motion can be found via the links below.
It is clear from these that contrary to Laithwaite's claims, circular motion does not have some force all of its own. Newton's laws can be applied to angular motion in 3-D and an important relationship obtained
This formula governs gyroscopic motion and is one of the tools used to explain what is happening in Laithwaite's videos.
Video 5: A toy gyroscope precesses on ice.
Video 6: A Gyroscope precesses on a long arm
Video 7: A Gyroscope hangs off the top of a table
Video 8: Precession of a gyroscope on an arm with a double pivot point
Video 9: A gyroscope hangs from the ceiling on a long string
Video 10: A small boy lift a gyroscope, and precesses on a rotating platform as he does so