Axis of Figure: Rigid Bodies, Rotation & MOI

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SUMMARY

The "axis of figure" refers to the rotational axis of a rigid body, particularly in the context of symmetrical tops, as discussed in Sommerfeld's Lectures on Mechanics. The quote provided illustrates that the gravitational torque is dependent on the distance between the fixed point and the center of mass, denoted as |L|=m*g*s*sin(theta), where theta is the angle between the vertical and the axis of figure. This axis is crucial for understanding the dynamics of rotation and moment of inertia in rigid bodies. The discussion clarifies that the axis of figure corresponds to the unequal moment of inertia in symmetrical tops.

PREREQUISITES
  • Understanding of rigid body dynamics
  • Familiarity with moment of inertia concepts
  • Knowledge of gravitational torque calculations
  • Basic principles of rotational motion
NEXT STEPS
  • Study the concept of moment of inertia in detail, focusing on symmetrical tops
  • Explore the derivation of gravitational torque in rigid body rotation
  • Learn about the implications of the axis of figure in various mechanical systems
  • Investigate Sommerfeld's Lectures on Mechanics for deeper insights into rotational dynamics
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Mechanical engineers, physics students, and anyone interested in the dynamics of rigid bodies and rotational mechanics will benefit from this discussion.

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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