Chapter 13, Problem 86CP

Using Figure 13.9, carefull 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 accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle $\epsilon$ , 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. $\tan \left(\lambda +\epsilon \right)=\frac{g}{g-{\omega }^2{R}_E}\tan \lambda$ , where $\omega$ is the angular velocity of Earth.