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How fast would the Earth have to spin for the centrifugal force to overpower gravity?
Abe995
Force of gravity = Mass (m) x acceleration due to gravity (g)
Force of gravity = mg Centrifugal Force = Mass (m) x Radius of Earth(r) x Angular Velocity2 (̉ۡ2)
Centrifugal Force = mr̉ۡ2 The acceleration due to gravity (g) = 9.80665 m/s2.
Radius of Earth = 63,78,100 m Lets consider an equilibrium where both the above forces are equal. * mg = mrÉ2 * g = rÉ2 * rÉ2 = g We have to find a value of É that satisfies the above equation * rÉ2 = g * 63,78,100 x É2 = 9.80665 * É2 = 9.80665 / 63,78,100 * É2 = 1.53753469 × 10-6 * É = 1.23997367 x 10-3 At this angular velocity, the centrifugal force is exactly equal to the gravitational force. If the earth spins any faster than this, the Centrifugal force will overpower the gravitational force. The current angular velocity of Earth is 7.2921150 × 10−5 radians per second.
The ratio of the required angular velocity to the current angular velocity is 17.0043077.
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∙ 14y ago
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