The earth revolves about its axis once every 24 hours and you with it. At our la

Question

The earth revolves about its axis once every 24 hours and you with it. At our latitude, the distance from our location (Miami) to the earth's axis of rotation is approximately 3311.77 km. Use this information to calculate our centripetal acceleration v^2/R. You need to find v and express it in km/h^2. You can do this by converting our speed of 1 revolution every 24 hours to so many kilometers per hour because you know the distance we travel in 24 hours: the circumference of a circle at our latitude. Before you execute, do you perceive this acceleration? Is there an experiment that you can think of that might give it away? After you think about this, do you expect a large value or a small one? Now execute and test your intuition.

Explanation / Answer

Speed is given by:

v = d/t

In the given case distance covered is d = 3311.77 km in 24 hours

v = 3311.77/24 = 138 km/h

centripital acceleration is given by

a = v^2/R

we need to know R,

2 pi R = 3311.77 =>R = 3311.77/2 x 3.14 = 527.35 km

a = v^2/R = 138^2/527.35 = 36.11 km/h^2

Hence, a = 36.11 km/h^2

this is a = 0.0028 in m/s^2, so yes its feasible and less acceleration.

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