Axis of Figure: Rigid Bodies, Rotation & MOI

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The "axis of figure" refers to the rotational axis of a rigid body, particularly in the context of a symmetrical top where the fixed point does not align with the center of mass. In Sommerfeld's Lectures on Mechanics, the gravitational torque is defined in relation to this axis, with the angle theta representing the inclination of the axis of figure to the vertical. The discussion highlights that there are infinite axes about which the figure can rotate, but the axis of figure is specifically associated with the unequal moment of inertia. The absence of visual aids in the text raises questions about the term's definition. Understanding this concept is crucial for analyzing the dynamics of rigid body rotation.
becko
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Hello. Can anyone tell me what is the "axis of figure" or "figure axis" ?
This is in the context of rigid bodies, rotation, and moment of inertia.
 
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Can you provide the actual quote? Does there need to be any more meaning to it than the obvious?

The figure in question would have (infinite) axes about which it could rotate i.e. anyone of them could be the rotational axis of the figure.
 
This is from Sommerfeld's Lectures on Mechanics. This is the quote

"For the heavy symmetrical top the fixed point O (point of support in the socket) no longer coincides with the center of mass G (located on the axis of symmetry); call s the distance OG. The magnitude of the gravitational torque is then:

|L|=m*g*s*sin(theta)

where theta is the angle between the vertical and the axis of figure."

I'm pretty sure that theta equals the angle between the vertical and the line OG. And, by the way, there not a single figure (as in picture) in the whole section where this quote is taken from. That's why I guess this term must have some definition.
 
I just found out that the axis of figure of a symmetrical top is the axis corresponding to the unequal moment of inertia.
 
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