# Equations for air drag acting on a body with both translational and rotational motion

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.