The Earth has a radius of 6380km and turns around once on its axis in 24hr. a) W

Question

The Earth has a radius of 6380km and turns around once on its axis in 24hr. a) What is the radial acceleration (acceleration pointing towards the center of the Earth) of the object at the equator? Give your answer in m/s^2 and also as a fraction of g b) If the radial acceleration a_rad is greater than g, objects will fly off the Earth's surface and into space (We will see why this is true in a couple of weeks). What would the period (time to complete one revolution) of the Earth's rotation have to be for this to occur?

Explanation / Answer

A) One complete revolution is 2 pi radians.

The earth revolves one complete revolution in 24 hours.

24 hours * 60 min/1 hr * 60 sec/1 min = 86400 seconds

The earth revolves at a rate of (2*pi)/86400 rad/sec = 7.27 e -5 rad/sec = w

r = radius of curvature = radius of the earth. 6380000 meters

angular acceleration = w^2* r

angular acceleration = (7.27 e -5)^2* 6380000 = 0.0333851 m/s2

angular acceleration = 0.0034 g

B)


First of all, force of gravity is not g, that is the acceleration due to gravity.

Fcentripedal = mV²/r
V is velocity
r is the radius
m is mass in kg

force of gravity is weight and is given by mg

so for them to be equal,
mg = mV²/r
V = (rg) = (6380000*9.8) = 7907 m/s

circumference of earth is 2 6380000 = 40090000 m
40090000 m / 7907 m/s = 5070 seconds for 1 revolution.

5070 sec = 1.4 hours

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