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If something weighs 10 kilos at one of the Earths poles, what will it weigh at the equator?

If something weighs 10 kilos at one of the Earths poles, what will it weigh at the equator? Don’t know if I’m right, but surely it must weigh slightly less, due to the centrifugal force (with the Earth’s rotation) counter-acting the Earth’s gravitational force? This question has bugged me for years, and at last I have an opportunity to ask someone who can ‘put my mind at rest’
BARRY WILKINSON from Tyne and Wear (Age 55+)

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One Response

  1. Kilogramme is defined as a unit of mass, which is a property of the item. Your item will have 10 kg mass in space or on the Earth.

    It will, however, not weigh the same as weight is the downward force on the mass. This is measured in force units and is what a normal weighing scales measures. A spring is compressed and the ammount of deflection depends on the force.

    As you correctly observe the force on a mass is not the same at all points on the Earth’s surface. I believe that more important than the centripetal acceleration is the distance from the centre of the Earth. The centrifugal force has spun our planet out at the middle as if it had had too many beers. As our planet is more like a satsuma than a cricket ball the ground is further from the centre at the equator than at the poles so the strength of gravity is lower. The difference is not very large so you will not have to calibrate your scales if you go on holiday, but does affect accurate measurements.

    An old style balance with a rod and two pans for weights compares the weights of two masses so would say your item weighs the same as a 10 kg test weight even on the moon.

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