Axis of rotation and rotating rigid body We know that angular momentum of a solid disk rotating with angular velocity $\omega$ is given by $I\omega$ about its center. Now if I chose any axis (parallel to above), will it have same magnitude of angular momentum as in the above case? If not how should I tackle this axis of rotation?
 A: When you talk about a rigid body the distance between any two points is fixed. That implies angular velocity w is same for all points. Now ony moment of inertia changes:
I=Icm+md^2 [d is distance between cm and the point]
This is the parallel axis theorem.
Get I and angular momentum=Iw
A: When youare talking about angular momentum about any axis(inluding one that passes through center of mass), you carry out the "formula":$\vec{L}=\vec{L_{com}}+I_{com}\vec{\omega}$ where direction of $\vec{L_{com}}$ and $I_{com}\vec{\omega}$ is to be kept in mind, during vector summation.While we calculate $\vec{L}$, about COM, $\vec{L_{com}}$ becomes zero because, PERPENDICULAR distance between COM and point of reference becomes zero.Also note that $\vec{L}$ about any axis is NOT equal to $I_{axis}\vec{\omega}$. This is ONLY true if and only if the body is actually rotating about that axis or the point of contact is instantaneously at rest at that point( i.e. the body is instantaneously rotating about that point, as is the case during pure rolling motion of a ball or body on ground). Now by parallel axis theomem we can calculate $$I_{axis} = I_{\mathrm{cm}} + md^2$$.
A: The angular momentum will be different: however, you will be able to calculate it with the parallel axis theorem.
Measure the distance from your new axis to the center of mass and call it $d$. Your new rotational inertia $I$ can be calculated from the rotational inertia around the center of mass $I_{\mathrm{cm}}$ using the formula:
$$I = I_{\mathrm{cm}} + md^2$$
There is a derivation of this formula on Wikipedia.
Once you have found $I$, you can just find angular momentum using the same formula you were before: $L=I\omega$, where $\omega$ is the angular velocity about the new axis (the one that doesn't pass through the center of mass).
