The motion of a rigid body Consider a rigid body with $n$ forces acting on it. What I intend to know is how to determine the motion of the body, more specifically:

*

*How to determine a point through which the axis of rotation of the body passes

*How to determine the direction in which the axis of rotation points

*How to determine the angular velocity of the body

I admit that answering these questions might be time consuming, so it would be helpful if you could provide some reading material which can answer these questions. Also, if you do intend to answer my question, please do provide some mathematical backing to it.
 A: The general 3D motion of rigid body is not simple; for example, inertia is a tensor. Euler developed the general solution.  Rotation in a plane where inertia is a scalar, is a simple special case addressed in most general physics books such as one by Halliday and Resnick.
The general case is developed in Goldstein, Classical Mechanics.
I find the online development in https://ethz.ch/content/dam/ethz/special-interest/mavt/mechanical-systems/mm-dam/documents/Notes/Dynamics_LectureNotes.pdf to be very helpful. This is an engineering based explanation.
A: *

*axis of rotation is passing through a point , with respect to which angular velocity of all the point on the body is same.

*this can be determined by right hand palm rule (used in cross product rule to determine the direction)->your thumb should point in direction of axis of rotation,four fingers in direction of point which is rotating and the palm will face in direction of velocity of that point, you will be given point , velocity and then you can finger the direction of thumb.
3)for this i will recommend you to watch "Rotational dynamics by Mohit Tyagi" on youtube(if you dont know hindi ,then you can see subtitle and understand the concept).

