Question

What is the maximum centripetal acceleration experienced by a person standing still on the surface of the Earth? Where must they be located?

Answer 1

Answer:

The person must be located in the Equator Line. The maximum centripetal acceleration experienced by a person is 0.0337 meters per square second.

Explanation:

Physically speaking, the centripetal acceleration ($a_{r}$), measured in meters per square second, experienced by a person is defined by the following expression:

$a_{r} = \omega^{2}\cdot r$ (1)

Where:

$\omega$ - Angular speed of the Earth, measured in radians per second.

$r$ - Distance perpendicular to the rotation axis, measured in meters.

Since rotation axis passes through poles and distance described above is directly proportional to centripetal acceleration. The person must be located in the Equator Line, which is equivalent to the radius of the planet.

In addition, the angular speed of the Earth can be calculated in terms of its period ($T$), measured in seconds:

$\omega = \frac{2\pi}{T}$ (2)

If we know that $r = 6.371\times 10^{6}\,m$ and $T = 86400\,s$, then the maximum centripetal acceleration experienced by a person is:

$a_{r} = \left(\frac{2\pi}{86400\,s} \right)^{2}\cdot (6.371\times 10^{6}\,m)$

$a_{r} = 0.0337\,\frac{m}{s^{2}}$

The maximum centripetal acceleration experienced by a person is 0.0337 meters per square second.