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we here at brilliant assume that you work through

We here at Brilliant assume that you work through these problems using some sort of writing utensil. Take your pen or pencil, balance it on its tip, and let go. It falls over. How fast in m/s is the other end of the pen or pencil going when it hits the table, assuming the tip doesn''t slip?

Details and assumptions
Model the pen/pencil as a uniform one dimensional rod of length 15 cm.

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