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Why is the direction of centrifugal force acting parallel to the equator rather than perpendicular to the centripetal force on 3D rotating spherical objects like the Earth?

picture of centrifugal force acting on Earth at different latitudes

I'm having trouble understanding this because in 2D planes, the centrifugal force acts perpendicular to the centripetal force by Newton's Law which makes intuitive sense. However, for rotating 3D objects this only applies at the horizontal 2D cross-section which passes through the centre of mass, whilst at different latitudes it no longer acts perpendicular to gravity but is parallel to the equator shown by the red arrows in the picture.

My physics is not very advanced, so I'd appreciate any intuitive and relatively simple explanation.

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enter image description here

Why is the direction of centrifugal force act parallel to the equator rather than perpendicular to the centripetal force on 3D rotating spherical objects like the earth

Because each particle performs circular motion about the line ZZ'. In my diagram particle m performs circular motion about point C which lie on line ZZ'.

Image Source : Google

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At all different latitudes on Earth you are always moving with the Earth's rotation perpendicular to the Earths axis. Therefore the centrifugal force is always perpendicular to the axis. The centripetal force of gravity always points towards Earths center, not its axis.

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