Does the gravity we feel equal G(M/r^2) - our centripetal acceleration

In summary, the Earth's rotation causes a centrifugal force that slightly reduces the weight experienced by objects at the equator compared to those at the poles. However, this difference is very small and may not be discernible. Some people define weight as the force with which Earth's gravity pulls on an object, in which case there would be no difference in weight between the two locations. However, for a perfectly spherical Earth, the difference in weight would be more noticeable due to variations in gravitational pull at different locations on the Earth's surface.
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D.Hayward
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We all know that something traveling in cicular motion at a constant speed has a centripetal acceleration towards the axis of rotation. I suppose this means we (travelling around the axis of rotation of the earth) also require a centripetal acceleration. This can be provided by gravity which is calculated by a=G(M/r^2) to be 9.81 m/s^2. However a portion of this has to be 'used' just to stop us drifting into space, this should be equal to our centripetal acceleration. Therefore shouldn't we feel 9.81 m/s^2 minus our centripetal acceleration in everyday life and in physics practicals. Is this true?
 
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Welcome to PF,

D.Hayward said:
We all know that something traveling in cicular motion at a constant speed has a centripetal acceleration towards the axis of rotation. I suppose this means we (travelling around the axis of rotation of the earth) also require a centripetal acceleration. This can be provided by gravity which is calculated by a=G(M/r^2) to be 9.81 m/s^2. However a portion of this has to be 'used' just to stop us drifting into space, this should be equal to our centripetal acceleration. Therefore shouldn't we feel 9.81 m/s^2 minus our centripetal acceleration in everyday life and in physics practicals. Is this true?

Yes. Basically. You would not "weigh" as much at the equator as you would at the poles. However, you have to be very precise about what the word "weigh" means here. More precisely, the Earth would not have to push up on you with as much normal force in order to support you, and so you would "feel" less heavy (although I'm don't think the difference is discernible). Some people define "weight" as this, in which case yes, you would "weigh" less by that definition. Others define your weight as the force with which Earth's gravity pulls on you, which would not be different between the two locations.* Under this definition, your weight is the same, even if the surface of the Earth doesn't have to support as much of it.

*for a perfectly spherical Earth, that is. In reality, Earth is not perfectly spherical and g varies with location on the Earth's surface.

http://curious.astro.cornell.edu/question.php?number=310
 
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Related to Does the gravity we feel equal G(M/r^2) - our centripetal acceleration

1. What is the equation for the force of gravity?

The equation for the force of gravity is F = G(Mm)/r^2, where G is the universal gravitational constant, M and m are the masses of the two objects, and r is the distance between them.

2. How is G related to the force of gravity?

G is a constant that is used to calculate the force of gravity between two objects. It is a fundamental constant in physics and its value is approximately 6.67 x 10^-11 Nm^2/kg^2.

3. What does the equation G(M/r^2) represent?

This equation represents the force of gravity between two objects due to their masses and the distance between them. It is also known as the inverse square law, which means that as the distance between the objects increases, the force of gravity decreases.

4. How is centripetal acceleration related to gravity?

Centripetal acceleration is the acceleration that a body experiences when it moves in a circular path. It is directly related to the force of gravity because it is the force that keeps objects in orbit around a larger mass, such as a planet or star.

5. Does the equation G(M/r^2) - our centripetal acceleration accurately represent the force of gravity?

Yes, this equation accurately represents the force of gravity between two objects as well as the centripetal acceleration experienced by an object in orbit around a larger mass. It is an important equation in understanding the effects of gravity in our universe.

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