P. mg SE RE Figure 13.9 For a person standing at the equator, the centripetal acceleration (ac) is in the same direction as the force of gravity. At latitude 1, the angle the between ac and the force of gravity is i and the magnitude of ac decreases with cosi.
Using Figure 13.9, carefully sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass, m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal acceleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle ε , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan(λ + ε) = (g / (g − ω2 RE)) . tanλ , where ω is the
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