# The Naked Scientists Forum

### Author Topic: Centrifugal forces and the earth.  (Read 1193 times)

#### Ricwed05

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##### Centrifugal forces and the earth.
« on: 10/01/2013 01:32:08 »
Earlier, I was wondering what affect centrifugal forces have on our 'weight' here on Earth.
I considered a knot on a piece of string which was being swung round and round.. If you were on the side of the knot facing away from the centre of spin you'd be pulled outwards from the knot, but if you were on the inside you'd be 'pulled' towards the knot.

Moving on from this analogy, I wondered if the effects of the change of directional velocity of the earth (and us) would have any effect on us. If you were, say, on a part of the world currently at midnight, would you be 'pulled' away from the earth due to the centrifugal forces present? and vice versa at mid day?

Tried to do some calculations.. (circumference of earth orbit/a year = speed, speed in one direction = speed in one direction*sine(time), differential of that = acceleration in one direction) got an answer of 1.24 m /s /s at any instant..

Not that I think that's right (seems far too big) I was wondering what effects it does have? Is it a completely negligible contribution? Am I just completely wrong in my understanding of centrifugal forces? not going to lie, haven't done much mechanics so that wouldn't be shocking haha.

Thank you for your time! :)

#### Pmb

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• Posts: 1838
• Physicist
##### Re: Centrifugal forces and the earth.
« Reply #1 on: 10/01/2013 03:06:53 »
Earlier, I was wondering what affect centrifugal forces have on our 'weight' here on Earth.
It decreases it the further you get towards the equator, of course.
I considered a knot on a piece of string which was being swung round and round.. If you were on the side of the knot facing away from the centre of spin you'd be pulled outwards from the knot, but if you were on the inside you'd be 'pulled' towards the knot.
I don't understand what you're trying to say. As measured from an inertial frame, anywhere on the string there is one force, the centripetal force = tension in string. In non-inertial frame there is the centrifugal force and the tension in the string.

#### evan_au

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##### Re: Centrifugal forces and the earth.
« Reply #2 on: 10/01/2013 10:34:54 »
I think maybe you are talking about "tides"?

Assuming an ideal Earth and Sun (perfect, non-rotating spheres of uniform density) and no Moon or planets...
• The Earth will be on a circular orbit with a 1-year period
• The Earth will accelerate towards the Sun as if all its mass were concentrated at the center of the Earth. This point will be in free-fall.
• The midnight side of the Earth will feel a slightly lower gravitational attraction towards the Sun than the center of the Earth does (inverse square law), so it will feel a reduced acceleration towards the center of the Earth+Sun
• The midday side of the Earth will feel a slightly higher gravitational attraction towards the Sun than the center of the Earth does, so it will feel a reduced acceleration towards the center of the Earth
• These effects result in the daily tides in ocean and land (land tides have lower amplitude due to the stiffness of rock).

If we add daily rotation of the Earth, the ocean (and eventually, land) would adopt the shape of a squashed sphere, moving from the poles (with higher acceleration to the center of the Earth) to the equator (which has reduced acceleration towards the center of the Earth).

Put them together, and you have a squashed sphere with twice-daily tides (or more complicated tides, if you add a Moon too).

#### AndroidNeox

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##### Re: Centrifugal forces and the earth.
« Reply #3 on: 13/01/2013 01:48:09 »
The rotation of the Earth does partially counteract the gravitational pull, particularly near the equator, which is why the Earth isn't exactly spherical, but is wider around the equator.

#### The Naked Scientists Forum

##### Re: Centrifugal forces and the earth.
« Reply #3 on: 13/01/2013 01:48:09 »