👉Logical Questions 😴
If 🌐 earth stops rotating, what is the value of 'g' at the equator?
Without rotation, Earth will not have equatorial bulge and its radius will go to its average radius of 6,371 km. The simplest way to get this answer is to use the notion of centrifugal force. When a body rotates about the center of the Earth, the action of inertia shows up as if an apparent centrifugal force is acting upon it pointing away from the center of the Earth in effect cancelling a very small part of the weight. The magnitude of that force is mv^2/R so the acceleration corresponding to it is v^2/R.
Average Radius of Earth = R= 6,371,000 m
Earth period = T = 24 hours = 24*3600 s = 86400 s
Equatorial velocity = V= 2(3.1416)R/T = 2*3.1416*6,371,000/86400 m/s = 463.3 m/s
Centripetal Acceleration = g1 = V^2/R = (463.3^2)/6,371,000 = 0.0337 m/s^2
You can compare that with current values of g which is 9.80665 at the poles and 9.77275 m/s^2 at the equator. The equatorial g will increase by amount g1 when not rotating and will be equal to polar g. The increase is only 0.34%.
If 🌐 earth stops rotating, what is the value of 'g' at the equator?
Without rotation, Earth will not have equatorial bulge and its radius will go to its average radius of 6,371 km. The simplest way to get this answer is to use the notion of centrifugal force. When a body rotates about the center of the Earth, the action of inertia shows up as if an apparent centrifugal force is acting upon it pointing away from the center of the Earth in effect cancelling a very small part of the weight. The magnitude of that force is mv^2/R so the acceleration corresponding to it is v^2/R.
Average Radius of Earth = R= 6,371,000 m
Earth period = T = 24 hours = 24*3600 s = 86400 s
Equatorial velocity = V= 2(3.1416)R/T = 2*3.1416*6,371,000/86400 m/s = 463.3 m/s
Centripetal Acceleration = g1 = V^2/R = (463.3^2)/6,371,000 = 0.0337 m/s^2
You can compare that with current values of g which is 9.80665 at the poles and 9.77275 m/s^2 at the equator. The equatorial g will increase by amount g1 when not rotating and will be equal to polar g. The increase is only 0.34%.
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