Centripetal acceleration

For an object moving in a uniform circular motion, the centripetal acceleration is

\begin{aligned} a=\frac{v^2}{r} \end{aligned}

Since v=r\omega ,

\begin{aligned} a&=\frac{r^2\omega ^2}{r} \\ &=r\omega ^2\end{aligned}

It is important to note that this centripetal acceleration is not angular acceleration. Angular acceleration is used in a rotational body while what we are doing here involves an object moving in a circle.

A body of mass m would experience a force of \begin{aligned} \frac{mv^2}{r} \end{aligned}

Earth’s gravitational acceleration

An object moving in a circular motion around Earth experiences a centripetal force. Since this force equals to the weight,

\begin{aligned} mg&=\frac{mv^2}{r}\\ g &= \frac{v^2}{r}\end{aligned}

We can see that the velocity of an object moving around Earth depends only on its distance from the Earth’s centre(radius).

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