# When applying the equation of torque and equating it to $I\alpha$ which moment of inertia do we take?

I believe $T=I_{cm}\alpha$, where $I_{cm}$ is the moment of inertia about centre of mass and $\alpha$ is the angular acceleration. But do we take $I_{cm}$ even if the torque has been taken about a point which is not the centre of mass? Would we then apply parallel axis theorem and find the new moment of inertia and use it in our equation? If no, then why not?

• The simplest equation of motion for rotation is $T=I\dot{\omega}$ where $I$ is the moment of inertia around the axis of rotation and $T$ is the torque around the axis of rotation. $\dot{\omega}$ is the angular acceleration resulting. – Gert Nov 14 '15 at 14:34