A. Suppose you stand on a bathroom scale at one of the Earth\'s poles, and it re

Question

A. Suppose you stand on a bathroom scale at one of the Earth's poles, and it reads 750.0 Newtons. If you stand on the same scale at the Earth's equator, and your mass in unchanged, what will be the scale reading on the equator? Assume that the Earth is a perfect uniform-density sphere of constant radius, and the g=9.8 m/s^2 everywhere on the surface of the non-rotating Earth.)

B. Suppose that you had the magical power to make the Earth spin faster or slower, as you desire. You decide to shorten the Earth's rotational period so that people living on the equator feel zero "apparant weight" (i.e., their bathroom scales all read zero). What rotational period (in hours) would be necessary to do that?

Explanation / Answer

mass = weight / g = 750 / 9.8 = 76.53 kg

a) Weight at equator = mg - m* omega^2 * R

here, R = 6378.14 km = 6378140 m

omega = (2*pi) / (24*3600) rad / s

=> Weight on equator = 747.42 N

b) For scales to read zero. We need omega such that weight becomes zero

=> 0 = mg -m* omega^2 * R

=> omega = sqrt (g / r)

Hence, rotational periiod = (2*pi) / omega

= (2*pi) /sqrt (g / r) = 5068.9015 seconds

= 1.408 hours or

= 1 hour 24 minutes and 28.9 seconds

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