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A pendulum will swing slowest when closest to the equator. Why is this?

The time period, T, of the swing of a pendulum is given by:

T=2π√(l/g)

where l is the length of the pendulum and g is acceleration due to gravity.

Because the Earth is spinning, there is a bulge at the equator and the poles are

slightly flattened. Hence on the equator the radius to the centre of the earth is

greater than the radius at the poles.

The equatorial radius is 6378.1km while the polar radius is 6356.8 km

The value of g at the Earth's surface relates to the values of the Earth's radius, r, at

that point using an inverse square law ie g is proportional to 1/r2

At the North Pole, g is about 9.83m/s2, while at the equator, g is smaller, at only

9.79m/s2 .

So the period of a pendulum will be longer (i.e. slowest) at the equator than at the

pole

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