Earth rotates on its axis once every 24 hours, so that objects on its surface ex

Question

Earth rotates on its axis once every 24 hours, so that objects on its surface execute uniform circular motion about the axis with a period of 24 hours. Consider only the effect of this rotation on the person on the surface. (Ignore Earth's orbital motion about the Sun.)
(a) What is the speed and what is the magnitude of the acceleration of a person standing on the equator?
v = m/s
a = m/s2

Express the magnitude of this acceleration as a percentage of g.
%
(b) What is the direction of the acceleration vector?
away from the center of Earth
directly at the center of Earth


(c) What is the speed and what is the magnitude of the acceleration of a person standing on the surface at 35°N latitude?
v = m/s
a = m/s2

(d) What is the angle between the direction of the acceleration of the person at 35°N and the direction of the acceleration of the person at the equator if both persons are at the same longitude?

Explanation / Answer

The radius of the earth, R = 6370 km
a)   The speed of the person = The distance traveled by the person/time elapsed

                                     = 2R/T = 1666.8 km/hr = 463 m/s

The acceleration is given by the formula, a = v^2/r = 0.034 m/s^2             a/g = 0.034/9.8 = 0.00343 = 0.343% b)   The direction of the acceleration vector directly at the center of Earth
c)   When the person is standing on the surface at 35 degree latitude then the radius is given by, r =R cos = 6370 cos35 = 5218 km            The speed of the person, v =  2R/T = 1365.3 km/hr = 379.3 m/s           The acceleration of the person, a = v^2/r = 0.03 m/s^2 d) The angle between the directions of the avveleration of the person at 35 degree of the acceleration of the person at the equator if both persons are at the same longitude is zero means they are parallel to each other

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