Question

How does external torque produce angular acceleration about the center-of-mass?

Answer 1

\[dL/dt=r \times F\] where L is an angular momentum \[L=I \omega\] and \[I\] is moment of inertia, \[\omega\] is an angular velocity, \[\tau = r \times F\] is a torque. So, if you differentiate \[\omega\] you get angular acceleration. \[I\] is a matrix in general.

Answer 2

\[\tau = r \times F = I \alpha\]

where \[ I \] is is moment of inertia,

where \[\alpha\] is angular acceleration