R-ATPHY-9

Guys did you know $g$ varies with altitude? That's crazy

And also Earth is an "oblate spheroid" so the radius is not the same everywhere!! Hence cause $g=\frac{GM}{r^{2}}$, as $r \uparrow$ then $g \downarrow$.

Also density of the rock?!?!? Changes $g$? Kinda crazy

Centripetal effect

• At the equator, some of the gravitational force is "used" to keep you in circular motion
• Hence, $g_{\text{actual}}=g_{\text{without rotation}}-\frac{v^{2}}{r}$
• Some of the object's weight is used to maintain a circular motion with Earth. We measure the gravity as less than it is.
• $\therefore$ acceleration down due to gravity is favoured.

Hence, at the equator:

$$\begin{align} a_{c}&=\frac{4\pi^{2}r^{2}}{T^{2}}\times \frac{1}{r} \\ &=\frac{4\pi^{2}r}{T^{2}} \\ &=\frac{4\pi^{2}(6370\times 10^{3})}{24\times 3600}^{2} \\ &=0.0336ms^{-2} \end{align} $$

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