Torque, angular momentum and a fixed axis-of-symmetry requirement

[rayoub]

I'm reading through "University Physics 14th edition" by Young and Freeman. Section 10.5 on angular momentum for a rigid body around a fixed axis of rotation is derived as L = Iω. However, it shows that this is only the case for the fixed axis of rotation being an axis of symmetry.

In section 10.2 on torque it is shown that torque for a rigid body around a fixed axis of rotation is τ = Iα. However, in this case, it doesn't mention the need for an axis of symmetry for this to be true. I'm wondering if it is just an omission or if there is a specific reason why there is no need for an axis of symmetry assumption in this situation.

Thanks for any guidance.

 

[hutchphd]

I don't know the book but here is the deal:

1. Both Torque τ and Angular Momentum L can be defined and calculated about any arbitrary axis as can the moment of Inertia I
2. If you know I about the Center of Mass then it can easily be gotten for other axes using the "parallel axis theorem"
3. The "principal moments of Inertia" are the C of M moments about the symmetry axes and can be used to generate any other direction. These are the axes where the object does not want to "wobble"when spun.

Why the book presents them this way I don't know precisely.