Understanding the Coriolis Force: How to Calculate It

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The Coriolis force is a result of the Earth's rotation, causing moving objects to deflect to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. It is not a real force but an apparent effect observed in a rotating reference frame. The Coriolis effect influences weather patterns, ocean currents, and ballistic trajectories. To calculate the Coriolis force, one can use the formula F_c = 2mvωsin(φ), where m is mass, v is velocity, ω is the angular velocity of the Earth, and φ is the latitude. Understanding the Coriolis force is essential for fields like meteorology and oceanography.
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Homework Statement
Find the perpendicular component of N in an inertial frame and in a non-inertial frame
Relevant Equations
newton equation for non inertial frames
I know that the perpendicular force is the Coriolis force, but I don't know how to get it

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Do you know what causes the Coriolis effect ? Why it exists. What is the other force ?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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