Radial acceleration of an object that is in ecuador

Question

A question which I could not solve.

The radius of earth is $6.371$ km. The earth is rotating around itself in $24$ hours. Then, calcuate the radial acceleration of an object that is in ecuador.

We know that

$$a_{r} = \frac{v^{2}}{r}$$

Given values

$$r = 6.371$$

$$a_{rad} = ?$$

$$v = ?$$

According to the solution

• The circumference of earth $=$ $v$ . period

I cannot apply it because I don't know how to find the velocity ($v$). Could you take a look?

Regards!

Answer 1

Circumference of earth $x$ is $$x=2\pi R=2\pi\times6731km=40030km$$ and $t=24h=24\times60\times60s=86400s$, then $$v=\dfrac{x}{t}=463\dfrac{m}{s}$$ and $$a=\dfrac{v^2}{R}=3.3\times10^{-2}\dfrac{m}{s^2}$$

Answer 2

Compute the circumference from the radius you know. You cover that distance in $24$ hours, so that gives you the speed. The point of being in Ecuador is that it is close to the equator, so you can use the radius to find the distance traveled in a day. At other locations you would need to multiply by the cosine of the latitude, but this is (close to) $1$ in Ecuador.