# Normal on a mass have different values at pole and equator

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1. Nov 21, 2015

### Angie Tom

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

2. Nov 21, 2015

### 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.

3. Nov 21, 2015

### Angie Tom

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?

4. Nov 21, 2015

### 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?

5. Nov 22, 2015

### Angie Tom

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?

6. Nov 22, 2015

### JeremyG

Very good. :)

7. Nov 22, 2015

### Angie Tom

T
Thanks a million Jeremy!