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We know that the equator has the highest centrifugal acceleration caused by the rotation of the earth (a = 0.034m / s2) but it is negligible because the vector of the acceleration of gravity is much greater (g = 9.81m / s2) and it is right in opposition to the centrifugal acceleration vector. This results in a net acceleration of g = 9,776m / s2 on the vertical axis. On the other hand, if we are located for example in the parallel 18 ° (which is where I am now) we have a centrifugal force of a = 0.032m / s2 but in this case, the centrifugal force is not parallel to the gravity vector creating an angle of 18 ° with respect to the vertical. (See figure 1) Scheme of forces acting on a body with mass m = 1Kg at the equator and the parallel 18 °

Figure 1

That means that a static pendulum with a mass 1Kg will behave according to figure 2 Scheme of forces acting on a pendulum of mass m = 1Kg in parallel 18 °

Figure 2

The resulting force scheme at the point of the ceiling where the pendulum hangs is seen in Figure 3 Diagram of forces at the point of the ceiling where the pendulum hangs

Figure 3

If the Sc force that restricts the horizontal component of the centrifugal force could be eliminated without eliminating the vertical component Sg, the pendulum would move southward with a slight acceleration but would undoubtedly move. In the case of a drone flying in place, we have that the vertical component Fg is matched to the lift force Sg. But there is no force in the horizontal component that restricts movement. Therefore the drone should move horizontally according to Figure 4 Diagram of forces of a drone flying in parallel 18 °

Figure 4

Then calculating the horizontal distance d that the drone would travel with the formula d=0.5*a*t^2 we have that in 1 minute the drone would move 17.8 meters south. In 10 minutes the drone would travel 1782m. This obviously does not happen in reality. What would be the possible reasons?

Qmechanic
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El péndulo de Moisés
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2 Answers2

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The angle at which a plumb line hangs is, by definition vertical. Because of the centrifugal component, the local vertical when continued downward will not pass through the center of the earth. The local vertical is, however, perpendicular to the surface of a body of water. The net effect is that that the earth is slighly non-spherical. It is an oblate spheroid. The surface of a body of water is an equipotential, so there is no sideways force tending to move the water, or any drone hovering above it.

mike stone
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I believe it is to do with the fact that you are not accounting for all possible forces on the drone in your example. Yes there may be a southward component of the Centrifugal force, but is that the only possible horizontal force acting on it? The answer is no. There is e.g. air resistance stopping it from very slowly drifting away.

This problem is the same as asking the following:

Why don't I fly off a merry-go round going at a slow speed? - There is a small centrifugal force pushing me away from the centre in my rotating frame of reference, so surely this must push me off?

The answer is friction stopping me from slipping off, and contributing to the Centripetal acceleration.

This may be a good example of why friction and reaction forces are important.

Garf
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