# Given a rigid object and forces/torques acting on the object, how can we know the axis of rotation the resultant rotational motion

In static rotational equilibrium cases, we learn that the reference axis for calculation of torque is arbitrary. But what if there is a net torque? We use the equivalent of Newton's 2nd law for rotational motion to predict the angular acceleration, but it does not give us the axis of rotation. If there are multiple possible axes of rotation for the same object, how do we know along which axis will the result rotational motion be if there's net torque?

• Rotation tends to prefer the axis with the largest moment of inertia as it is the most stable orientation. – Sam Jul 7 '20 at 9:13
• is there a formal rule/law for this? – forgodsakehold Jul 8 '20 at 8:24
• None that I am currently aware of but it can be derived. – Sam Jul 9 '20 at 5:12
• oh, how can this be derived? any leads like URLs, or book references will do – forgodsakehold Jul 11 '20 at 5:49
• There is a derivation here and here. – Sam Jul 11 '20 at 14:07