Axis of Figure: Rigid Bodies, Rotation & MOI

[becko]

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.

 

[DaveC426913]

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.

 

[becko]

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.

 

[becko]

I just found out that the axis of figure of a symmetrical top is the axis corresponding to the unequal moment of inertia.

 

[PJC01]

The "axis of figure" or "figure axis" refers to the imaginary line around which a rigid body rotates. In other words, it is the line that passes through the center of mass of the object and is perpendicular to the plane of rotation. This axis is important in understanding the rotational motion of a rigid body, as it determines the direction and magnitude of the object's rotational inertia, also known as moment of inertia. The moment of inertia is a measure of an object's resistance to rotational motion and is dependent on the mass distribution of the object about its axis of rotation. The figure axis plays a crucial role in determining the moment of inertia and therefore, is an essential concept in the study of rigid body dynamics.