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Imagine you drop a very thick pencil. The pencil will fall with both linear velocity and angular velocity. How can we account for the drag forces acting it so as to calculate its angular velocity and centre of mass velocity at any given time?

We know that the equation for linear drag is simply $$F=kv$$ or $$F=kv^2$$ where $k$ is some constant for linear air drag.

We also know that the equation for angular drag is $$F=c\omega $$ or $$F=c \omega^2$$.

Is there anyway to combine the both for an object with both rotational and translational motion? Thank you.

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I am not sure what exactly you want to do but you can study motion in terms of translation of center of mass and rotation about center of mass in cases of combined translation and rotation.

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