Foucault Pendulum Vector Diagrams - Forty-five-degrees North Pendulum

Forty-five-degrees North Pendulum

For the 45° North pendulum with longitudinal swing (Figure 3A) the support point of the pendulum swing is moving along with the direction of rotation and the surface velocity vectors on either side of the swing are not balanced. The rotation of the Earth is observable in relation to the pendulum swing because a change in relationship to the surface occurs. At the south end of the pendulum swing the surface velocity vector (as projected to the center of the Earth) is that of the Equator, equal to 1 EVU. At the north end of the swing the velocity (as projected to the center of the Earth is that of the North Pole, equal to zero since zero distance is traveled in relation to the spinning Earth. Even though the surface velocities are different the angular velocities underneath the pendulum swing are all the same for this orientation.

For the 45° North pendulum with latitudinal swing (Figure 3B) the support point of the pendulum swing is moving along with the direction of rotation and the surface velocity vectors on either side of the swing are not balanced. The rotation of the Earth is observable in relation to the pendulum swing because a change in relationship to the surface occurs. On one side of the pendulum swing the surface velocity vectors are angled upwards and to the side but on the other side the vectors are angled downwards and to the opposite side. Since these vectors are not all in the same plane as the pendulum swing and are not balanced in the same direction there is a change in relationship between the surface and the plane of the pendulum swing.

Note: The schematic directly underneath the front view of the pendulum diagram is for velocity vectors projected towards the center of the Earth rather than straight down. It is much easier to interpret the magnitude of the vectors using the straight down projection that is shown on the right side of the diagram (the view from the top).