Rotation of earth and weight of an object on the earth

In summary, the rotation of the Earth does have an effect on the apparent weight of an object, with the net acceleration being different from the standard gravitational acceleration. This is due to the resolution of gravity's force into a centripetal force that acts parallel to the equator. The ratio of centrifugal to gravitational effects on an object's apparent weight can be calculated using the planet's radius, mass, and rotation period, resulting in a slight difference in weight at different latitudes. In fact, at the equator, the apparent weight is slightly less than the standard gravitational weight by about 0.34%. Thus, if the Earth were to stop its rotation, a person weighing 200 pounds at the equator would experience a slight increase
  • #1
manjuvenamma
102
0
We all know that g is more at the poles than at the equator because it is closer to the cenre. I think Earth's rotation will not have any effect on the g because g depends only on the mass product and the distance only.

But roration of the Earth should be having some effect on the weight of a body as it may have a component in the direction of g and the net acceleration will be different from g. How does this net acceleration that determines the apparent of weight of an object on the Earth change with the location (poles or equator) of the object on the Earth and the angular velocity of the rotation?
 
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  • #2
Have you ever solved the standard kinematic problem of a rollercoaster at the top of a loop? If you have, it is the same problem here with what you are asking.

Zz.
 
  • #3
manjuvenamma said:
But roration of the Earth should be having some effect on the weight of a body as it may have a component in the direction of g and the net acceleration will be different from g. How does this net acceleration that determines the apparent of weight of an object on the Earth change with the location (poles or equator) of the object on the Earth and the angular velocity of the rotation?
Start by drawing a free body diagram for the object. (Imagine that it's suspended on a string and you want to find the tension in the string--that would be the apparent weight of the object.) Now apply Newton's 2nd law. If the Earth didn't rotate, the acceleration in all directions would be zero. But if you include the rotation of the earth, you'll have an acceleration directed towards the axis of rotation (a centripetal acceleration).

First analyze the cases where the object is on the equator or on a pole, then worry about the locations in between.
 
  • #4
manjuvenamma said:
We all know that g is more at the poles than at the equator because it is closer to the cenre. I think Earth's rotation will not have any effect on the g because g depends only on the mass product and the distance only.

But roration of the Earth should be having some effect on the weight of a body as it may have a component in the direction of g and the net acceleration will be different from g.
This is probably just a matter of terminology, but often it is the net acceleration (including Coriolis and centripetal effects) that is called 'g'.

Furthermore, g does not depend on a mass product. There is only one mass involved in an expression for gravitational g, the mass of the earth.
 
  • #5
FYI, there is a related thread at

https://www.physicsforums.com/showthread.php?t=231193

where the ellipticity of a planet due to rotation is calculated.

The ratio of centrifugal to gravitational effects on an object's apparent weight is given by the ratio

[tex]
\frac{4 \pi^2 r^3}{GMT} \cos(\theta_{Lat})
[/tex]

where r, M, and T are the planet's radius, mass, and rotation period, respectively. [tex]\theta_{Lat}[/tex] is the latitude.

For the Earth this works out to 1/290 or 0.34% at the equator.
 
  • #6
Yes it does have an effect..
This is due to the gravity's force is resolved into a centripetal force that acts parallel to the equator.

Thus, At the Poles, apparent weight is the same as mg.

At the equator, Apparent weight
is g' = g - Rw^2
Where w is the angular velocity

At latitude 0 above the equator is
g' = √(g2+(Rw2-2g )Rw2 cos2ѳ)
 
  • #7
ok, so I guess I'm not following this correctly, if I weighed 200 pounds at the equator, and the Earth stopped it's rotation, how much would I weigh?
 
  • #8
jcarlisle said:
ok, so I guess I'm not following this correctly, if I weighed 200 pounds at the equator, and the Earth stopped it's rotation, how much would I weigh?
Your apparent weight would increase by mRω². As Redbelly98 stated in post #5, that's an increase of about 0.34%. Thus your apparent weight would increase by about 0.7 lbs.
 
  • #9
So the take-away here is that supermodels should all be told these facts so that they migrate to mountaintop observatories, where astrophysicist and astronomers can have their way with the shivering lasses. :rofl:

Or... yes, your weight would increase. My point however is that the effect of gravity drops off so with distance from the mass, that distance from the surface of the Earth is a much bigger issue than where on Earth you are. Better yet, you ignore psuedo-forces this way, and the models...
 

1. How does the rotation of the earth affect the weight of an object on its surface?

The rotation of the earth causes a centrifugal force that slightly reduces the weight of an object at the equator. This is due to the fact that the object is moving in a circular motion with the earth, and the centrifugal force counteracts the force of gravity slightly. However, this effect is very small and does not significantly impact an object's weight.

2. Does the weight of an object on the earth change at different latitudes?

Yes, the weight of an object on the earth does change at different latitudes. This is due to the fact that the earth is not a perfect sphere, but rather an oblate spheroid. This means that the earth bulges slightly at the equator and is flatter at the poles. As a result, the force of gravity is slightly stronger at the poles, making an object weigh slightly more there compared to the equator.

3. How does the rotation of the earth affect the weight of an object at different altitudes?

The rotation of the earth does not have a significant effect on the weight of an object at different altitudes. This is because the distance from the center of the earth to the object does not change significantly with altitude. Therefore, the force of gravity remains relatively constant and does not significantly impact an object's weight.

4. Does the weight of an object on the earth change over time due to the rotation of the earth?

No, the weight of an object on the earth does not change over time due to the rotation of the earth. While the earth is constantly rotating, the force of gravity remains constant and thus an object's weight does not change. Any changes in weight over time are due to other factors, such as changes in mass or location.

5. How does the rotation of the earth affect an object's weight on other planets?

The rotation of the earth has no direct effect on an object's weight on other planets. The weight of an object is determined by the mass and radius of the planet, not its rotation. However, the rotation of a planet can indirectly affect an object's weight by causing variations in the planet's gravitational field, which can impact the object's weight.

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