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Dazed&Confused
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Homework Statement
A pendulum is at rest with its bob painting toward the center of the earth. The support of the pendulum is moved horizontally with uniform acceleration [itex] a [/itex], and the pendulum starts to swing. Neglect the rotation of the earth. Consider the motion of the pendulum as the pivot moves over a small distance [itex] d [/itex] subtending at angle [itex] \theta_0 ≈ d/R_e << 1 [/itex] at the center of the earth. Show that if the period of the pendulum is [itex] 2\pi \sqrt{R_e/g}[/itex], the pendulum will continue to point toward the center of the earth, if effects of order [itex] {\theta_0}^2[/itex] and higher are neglected.
The Attempt at a Solution
I am not clear on how to tackle this. First of all, if the period of the pendulum for small angles is approximatly [itex] 2\pi \sqrt{R_e/g}[/itex], then the moment of inertia is [itex]m{R_e}^2[/itex]. This cannot be realistic for a simple pendulum. The question is part of an accelerated reference frame chapter so the forces on the pendulum in that frame are [itex]-ma[/itex] and [itex]mg[/itex]. Any further advice would help. Thank you.
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