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.
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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