Kater's pendulum

Since at least 1965, the Cavendish laboratory Physics course included an experiment to measure g to better than 1 part in 10,000 using Kater's pendulum. The pendulum (shown lying down, above) is hung vertically and pivots on a knife edge that rests on glass.

I measured the period of one pendulum, estimated its radius of gyration, and plotted an inferred graph of T^2 versus l. The two knife edges are at about -25cm and +69cm. The period of the pendulum was about 2 seconds. The pendulum has a large metal mass at one end. The opposite end has an exactly equal sized but very light wooden mass. [Why? see below.] The centre of mass is about one quarter of the way along the space between the knife edges. The knife edges and two other masses are adjustable, but you are encouraged to leave the knife edges where they are (maximally separated), and use the little masses to adjust the two periods. One movable mass is made of metal and one of wood. They have identical shapes like the larger metal and wood masses.
The experimental instructions are reproduced (poorly) below, along with the two pages from Squires's book that are referred to.
kater1.jpg ---- (112K): instructions
kater2.jpg ---- (91K): instructions
squires1.jpg ---- (24K): Squires's textbook
squires2.jpg ---- (25K): Squires's textbook
tsquared.gif ---- (4K): graph

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Why the pendulum has the spurious massless wooden lump on its light end. It's because the pendulum motion has extra associated air mass movement (similar in effective mass to the displaced air, cf ideal fluids moving past a sphere), which needs to be identical for the two configurations, otherwise the kinetic energies are not equal. The density of air is about 1/10,000 the density of steel, so this effect kicks in at the 1e-4 level that the pendulum is supposed to be measuring.
David MacKay <mackay@mrao.cam.ac.uk>
Last modified: Tue Dec 12 16:38:07 2000