Angular momentum finding the principle axis

[SpartanG345]

If an object is rotating about the axis of symmetry
and you are trying to find the angular momentum about the mass centre g.

Does a rotation about the axis of symmetry correspond to a rotation about the principle axis?

For this question i am trying to find the angular momentum about the mass centre of cone which is rotating about its axis of symmetry. However the axis of rotation is also rotating about the z axis.

Does the angular velocity w effect the angular momentum about the mass centre? I am guessing it would...

The only thing i am not sure about weather or not angular momentum about G would be evaluated about the principle axis

 

[tiny-tim]

Hi SpartanG345!

(btw, it's principal axis, like the principal of your school )

For this question i am trying to find the angular momentum about the mass centre of cone which is rotating about its axis of symmetry. However the axis of rotation is also rotating about the z axis.

Every axis of symmetry is a principal axis.

The principal axes of a cone are its centre line, and every direction perpendicular to that line.

To find the angular momentum, you must first find the angular velocity …

if that is along a principal axis, then just multiply by the moment of inertia; if not, then use the tensor method.