physics
posted by joseph on .
Believe it or not, a plumbbob does not hang exactly along a line directed to the centre of the Earth! Determine how far off true plumb a bob hangs in Cape Town. In which direction is the deviation (north, east, south, or west)? How would your answer differ for a plumbbob in London? (Assume that the Earth is spherical.)

What is centripetal acceleration as a function of latitude?
w = 2 pi/24 hours = 2 pi /(24*3600) rad/s
Ac = w^2 r
r = Re cos (Lat)
where Re is earth radius and Lat is latitude angle
calculate Ac
call tension in plumb bob line T
then T will be off the direction to center of earth by angle A
T vector  mg vector = m Ac vector
draw those with mg toward earth center and Ac horizontal toward earth NS axis
Then T cos A = m Ac cos Latitude +mg
and T sin A = m Ac sin Latitude
approximate T by m g
then sin A = (Ac/g) sin Latitude approximately 
4.7 degrees