Jim asked in Science & MathematicsPhysics · 1 month ago

# Shouldn't people weigh less at the north pole than on the equator?

If earth's gravity suddenly ended, people on the earth's equator would be flung off into space at 24,000 miles per hour. There are enormous centrifugal forces acting on everything at the equator, but not at the poles. It appears then that gravity is a different kind of force if it is impervious to centrifugal forces.

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• ?
Lv 6
1 month ago

Yes you do, because at the equator the centrifugal force due to the spinning of the Earth is at its maximum, and vanishes at the poles. ... If you weighed 100 pounds at the north pole on a spring scale, at the equator you would weigh 99.65 pounds, or 5.5 ounces less.

• 1 month ago

Gravity is NOT impervious to centrifugal force.  How did you make that conclusion?

Centrifugal force at the equator actually cancels some gravity and makes people weigh less.  A second reason people weigh less at the equator is the bulge which

makes them farther from Earth's center than at the poles.

• 1 month ago

No.  At the poles they are closer to the centre increasing the ACTUAL force of gravity.  At the equator some force is needed to keep the person on the surface leading to a lower APPARENT force of gravity.

There ARE no centrifugal forces. Gravity is not immune to Newton's laws.

• Dixon
Lv 7
1 month ago

There is an upward centrifugal force but due to the extremely slow rotation of one revolution per day the variation between poles and equator is quite small - but still measurable with good equipment. Note tho that few people live close to the poles.

• 1 month ago

Let's assume you're talking about the geographic north as opposed to the magnetic north which wanders around a bit.

Weight, the measurement, is the normal force acting on the body.  Since the Earth spins at a rate of about 1/86,400th revolutions or about 0.000073 radians per second, and you are about 6,371 km away from the axis of rotation at the equator, you would need an acceleration of about 0.0336 m/s^2 towards the center of the Earth to keep you rotating around it.  Since this centripetal force comes from the gravitational pull of the Earth on your body, then the resulting normal force on your body will be less at the equator than at the poles, by about 0.3%, because at the pole, your distance from the axis of rotation is very small.

Weight, the force, is the force of gravity pulling on the mass of the body.  It is proportional to the masses involved and inversely proportional to the square of the distance between them.  Since you are actually about 21 km further from the center of the Earth at its equator than you are at its poles, you actually have less weight at the equator.

So in both instances, as a measurement and as a force, you weigh less at the equator than at the poles.

• 1 month ago

you have it backwards. Objects at the equator weigh less than at the poles. By about 0.3%.

"gravity is a different kind of force if it is impervious to centrifugal forces" of course that is true. But what we measure is actually a combination of gravity and centripetal forces. And gravity as measured is not constant due to mass concentrations, altitude, and the shape of the earth (it has an equatorial bulge)

The variation that we measure is due to the centripetal force at the equator resulting from the earth's rotation and due to the fact that sea level at the equator is higher than the same level at the poles, due to the centripetal bulge of the earth.

So a 100 kg mass object would weigh 981 N. at the equator and about 984 N at the poles. (approximately, value varies as you move about on the earth surface)

• 1 month ago

I think you have it backwards as far as your thinking.  Less outward force at the poles so weight ought to be higher, if rotation is the only difference.  That is, if the downward force of gravitational attraction is the same everywhere, then clearly removing the outward force, the opposing force to gravity, will make the net downward force, or weight, be HIGHER (no upward pull to reduce weight).

The odd thing about the earth, though, is that we see it in terms of water level, sea level. We do not measure distance from center of the earth or rate of rotation.  We look to the sea, and say "sea level is the zero elevation".  Water, of course, is a fluid and makes a surface that is an equipotential line, meaning that sea level is where "weight" of water is the same (it moves if it is not). If there is some reason for forces to differ in a region, the water level will rise or fall until it hits that same "weight" level that exists all around the earth.

This means that if there is higher outward force at play, then water would change elevation until the mass beneath created enough gravity to offset that change in outward push.  And thus, the world is an oblate spheroid, almost round but flat on the poles and squished out at the equator.  We down here do not notice it, because our mark of level (sea level) is itself not level.  We just have always assumed that it is, because it sure seems that way from our perspective.  Turns out we were wrong.