What is the radial acceleration of an object at the earth's equator? Give your answer as a fraction of g
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The radial acceleration of an object at the earth's equator can be calculated using the formula:
aradial = ω^2 * r
where ω is the angular velocity and r is the radius of the Earth.
The angular velocity of the Earth is approximately 2π radians per 24 hours. In terms of seconds, this is:
ω = (2π radians/24 hours) * (1 hour/60 minutes) * (1 minute/60 seconds) = (2π/86400) radians per second
The radius of the Earth is approximately 6,371,000 meters.
Using these values, we can calculate the radial acceleration:
aradial = (2π/86400)^2 * 6,371,000 m
aradial ≈ 0.0337 m/s^2
To express this as a fraction of g, we divide the radial acceleration by the acceleration due to gravity at the Earth's surface (approximately 9.8 m/s^2):
Fraction of g = 0.0337 m/s^2 / 9.8 m/s^2
Fraction of g ≈ 0.0034
Therefore, the radial acceleration of an object at the Earth's equator is approximately 0.0034 times the acceleration due to gravity.