Normal on a mass have different values at pole and equator

[Angie Tom]

why does the normal on a mass have different values at pole and equator

 

[JeremyG]

This requires an understanding of circular motion and centripetal force. Draw out a free-body diagram as such:

- A circle representing the Earth;
- A rectangular block representing a man (or any mass) standing at the equator;

Recognize that the Earth is spinning about an axis passing through its centre, then think about what are the forces acting on the man?
What is/are the force(s) contributing to the centripetal acceleration of the man such that he can travel in a circular motion around the Earth's equator?
Finally, write out an equation relating the forces with the centripetal force (as the net force). Rearrange the terms of the equation such that you get:
N = ...

Now do the same but replace the man at the equator with another rectangular block at the pole. Again, find an expression N = ...

Compare the two expressions for N and you shall see why the normal contact force is different at the poles and at the equator.

 

[Angie Tom]

This requires an understanding of circular motion and centripetal force. Draw out a free-body diagram as such:

- A circle representing the Earth;
- A rectangular block representing a man (or any mass) standing at the equator;

Recognize that the Earth is spinning about an axis passing through its centre, then think about what are the forces acting on the man?
What is/are the force(s) contributing to the centripetal acceleration of the man such that he can travel in a circular motion around the Earth's equator?
Finally, write out an equation relating the forces with the centripetal force (as the net force). Rearrange the terms of the equation such that you get:
N = ...

Now do the same but replace the man at the equator with another rectangular block at the pole. Again, find an expression N = ...

Compare the two expressions for N and you shall see why the normal contact force is different at the poles and at the equator.

This is what I got!
No centripetal force on the mass at the pole as normal is equal to the gravitational force since the mass isn't orbiting in a circle! Its actually revolving around itself!
Right?

 

[JeremyG]

Correct. And what about the situation where the man is standing at the equator?

And finally, where is the normal contact force the greatest? The poles or the equator?

 

[Angie Tom]

Correct. And what about the situation where the man is standing at the equator?

And finally, where is the normal contact force the greatest? The poles or the equator?

At the equator the normal is equal to the difference between the gravitational force and the centripetal force.
At the pole, normal is equal to weight and so normal is greater at the pole?

 

[JeremyG]

Very good. :)

 

[Angie Tom]

T

Very good. :)

Thanks a million Jeremy!