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A pendulum whose upper end is attached so as to allow the pendulum to swing freely in any direction can be used to repeat an experiment first shown publicly by Foucault in Paris in 1851. If the pendulum is set oscillating, the plane of oscillation slowly rotates with respect to a line drawn on the floor, even though the tension in the wire supporting the bob and the gravitational pull of the Earth on the bob lie in a vertical plane. (a) Show that this is a result of the fact that the Earth is not an inertial reference frame. (b) Show that for a Foucault endulum at a latitude e, the period of rotation of the plane, in hours, is 24 sin θ. (c) Explain in simple terms the result at θ = 90° (the poles) and θ = 0° (the equator).

A pendulum whose upper end is attached so as to allow the pendulum to swing freely in any direction can be used to repeat an experiment first shown publicly by Foucault in Paris in 1851. If the pendulum is set oscillating, the plane of oscillation slowly rotates with respect to a line drawn on the floor, even though the tension in the wire supporting the bob and the gravitational pull of the Earth on the bob lie in a vertical plane.
(a) Show that this is a result of the fact that the Earth is not an inertial reference frame.
(b) Show that for a Foucault endulum at a latitude e, the period of rotation of the plane, in hours, is 24 sin θ.
(c) Explain in simple terms the result at θ = 90° (the poles) and θ = 0° (the equator).

Grade:11

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