Centrifugal Force Homework: Relationship to Radius?

[nobleman]

Homework Statement

Hi,
I am confused about the relationship between the centrifugal force and radius.
The centrifugal force equation for an object having constant mass and angular velocity moving around the Earth on GRS80 reference is Fc = m w^2/r (m=mass, w^2=angular velocity of the earth, r=earth's radius)
From this equation, the centrifugal force would have an inverse proportion to the Earth's radius, but logically as the radius decreases the centrifugal force would decrease until we reach the center which no force would be there.
Can anyone explain this issue and how the graph in this case would be?

 

[berkeman]

Homework Statement

Hi,
I am confused about the relationship between the centrifugal force and radius.
The centrifugal force equation for an object having constant mass and angular velocity moving around the Earth on GRS80 reference is Fc = m w^2/r (m=mass, w^2=angular velocity of the earth, r=earth's radius)
From this equation, the centrifugal force would have an inverse proportion to the Earth's radius, but logically as the radius decreases the centrifugal force would decrease until we reach the center which no force would be there.
Can anyone explain this issue and how the graph in this case would be?

Welcome to the PF.

Re-check your equation -- I think you got the "r" in the wrong place...

http://en.wikipedia.org/wiki/Centrifugal_force

.

 

[nobleman]

Thanks berkeman for your quick response, and it seems logical if r would be in the numerator, but I double checked the formula in the textbook and it is as I wrote
Please check these also
http://phun.physics.virginia.edu/topics/centrifugal.html
http://www.engineeringtoolbox.com/centripetal-acceleration-d_1285.html
I am still confused

 

[berkeman]

Thanks berkeman for your quick response, and it seems logical if r would be in the numerator, but I double checked the formula in the textbook and it is as I wrote
Please check these also
http://phun.physics.virginia.edu/topics/centrifugal.html
http://www.engineeringtoolbox.com/centripetal-acceleration-d_1285.html
I am still confused

You're mixing up the two forms of the equation:

$$F_c = \frac{mv^2}{r} = m {\omega}^2 r$$

These are the two forms that you can use -- which you choose depends on the problem at hand. They are equivilant because

$$v = \omega r$$
The wikipedia link that I posted earlier has the formulas correct.

.

 

[nobleman]

I believe you are absolutely right and I am really mixing up between the two equations. The textbook is wrong though by putting the formula form in the way I wrote at first and that's why I had this confusion in the first place.
Thank you so much for clearing this out