Calculating Deflection of a Plumb Bob due to Rotation of Earth

AI Thread Summary
The discussion centers on the deflection of a plumb bob due to Earth's rotation, highlighting that it may not align perfectly with gravitational force. The formula for deflection A at latitude L is derived as A = sin2L[(2(pi^2)R)/(gT^2)], where R is Earth's radius and T is the rotation period. The maximum deflection occurs at a specific latitude, while the deflection is zero at the poles and reaches its maximum at the equator. Participants suggest starting with a diagram to visualize the relationships involved in the calculations. Understanding these concepts is crucial for accurately determining deflection based on geographic location.
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Because of the rotation of the Earth, a plumb bob may not hang exactly along the direction of the Earth's gravitational force on the plumb bob but may deviate slightly from that direction.
a) Show that the deflection A in radians at a point at latitude L is given by

A = sin2L[(2(pi^2)R)/(gT^2)]

where R is the radius of the Earth and T is the period of Earth's rotation.

b) At what latitude is the deflection a maximum? How much is this deflection?

c) What is the deflection at the poles? At the equator?



Any ideas of where I can start with this?

Thanks
 
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Its always best to draw a diagram of these things first as you can right down several relationships which might get you going. What do you have so far?
 

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