- #1

Clara Chung

- 304

- 14

## Homework Statement

My book said:

As the Earth is rotating about its axis, objects on the Earth's surface are performing circular motion. Therefore, objects on the Earth are accelerating and they need a centripetal force. The weight contributes a small portion to the centripetal force needed. Therefore, the measured g is smaller. The decrease in g is largest at the equator. At higher latitude, the radius of the circle is smaller while w is the same. Therefore, the centripetal force needed is smaller. The measured g is larger at higher latitude.

## Homework Equations

## The Attempt at a Solution

However from my calculation, let the latitude be θ, W=weight, N=normal force, R=radius of the earth

Wcosθ - Ncosθ = mw^2 Rcosθ

W-N=mw^2(R)...(1)

Wsinθ=Nsinθ

W=N...(2)

Which is totally the same as considering an object on the equator.

Why am I wrong, please help