Coriolis Force Consider a simplified scenario where the Earth does not have a ro

Question

Coriolis Force

Consider a simplified scenario where the Earth does not have a rotational axial tilt with respect to its orbit around the sun. Further imagine that the solar system does not have an axial tilt with respect to the orbit of the sun around the galactic center.

Q #1: Compute magnitudes and directions for the Coriolis forces due to the rotation of the Earth about its axis, the revolution of the Earth about the sun, and the revolution of the solar system about the galactic center in each of the following scenarios:

i. Standing at the equator firing a cannon straight up (perpendicular to the surface of the Earth) at velocity v .

ii. Standing at the geographic North Pole firing a cannon straight up at velocity v .

iii. Standing at the equator firing a cannon horizontally (so that it would arc toward the North Pole) at velocity v .

iv. Standing at the geographic North Pole firing a cannon horizontally (so that it would arc toward the equator) at velocity v .

Q #2: Repeat Q #1 except this time you will consider the Centrifugal force. Note that you only need to consider your position (equator or pole) because particle velocity is unimportant for determination of the magnitude and direction of this force.

Explanation / Answer

1.First of all we have to understood that, how we find the direction of coriollis acceleration.
We find the coriollis where the sliding motion is supported with the rotational motion.
Direction of the coriollis will be at an angle of 90 degree in the sense of the direction of rotation.
The magnitude of the coriollis acceleration is = 2vw
where v is the velocity of sliding motion and w is the angular velocity of rotation.
(i) in this case rotation will be zero therefore coriollis will be zero.
(ii) At north pole when it moves in the vertical direction and earth rotates in the anticlockwise direction
therefore the direction will be -X axis.
(iii) At the equator rotation is zero therefore no coriollis.
(iv) Since canon is fired horizontally and we have to rotate it by 90 degree in the anticlockwise direction
therefore coriollis will be in the +Y direction

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