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The earth rotates. The ball falls in an latitude, not equator, let say in Germany. I am trying to understand how to express the ball in terms of the angular velocity on the planet. The constant rotation $w$ keeps the ball on the same latitude but the longitude changes hence needing some correction to the $\hat i$ -term and $\hat k$ -term. The right solution is $w [\sin(\lambda),0,\cos(\lambda)]$ but I cannot see it. $\hat i$ is projected to the z -axis. $\hat k$ is projected to the x -axis, though but I cannot differentiate them yet.

How to express the falling ball in terms of the constant angular velocity $\bar w$?

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