Axis of Figure: Rigid Bodies, Rotation & MOI

In summary, the "axis of figure" or "figure axis" refers to the rotational axis of a symmetrical top, which may not necessarily coincide with the center of mass. It is defined as the axis corresponding to the unequal moment of inertia and is mentioned in Sommerfeld's Lectures on Mechanics. The term is used in the context of rigid bodies, rotation, and moment of inertia.
  • #1
becko
27
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
I just found out that the axis of figure of a symmetrical top is the axis corresponding to the unequal moment of inertia.
 
  • #5


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.
 

What is the definition of "Axis of Figure"?

The Axis of Figure refers to an imaginary line around which a rigid body rotates or spins. It is also known as the axis of rotation or axis of symmetry.

How do you calculate the Moment of Inertia (MOI) for a rigid body?

The Moment of Inertia (MOI) is calculated by integrating the mass of each individual particle in a rigid body with respect to its distance from the axis of rotation. This integral is represented by the formula I = ∫ r² dm, where r is the distance from the axis of rotation and dm is the mass element.

What is the relationship between MOI and rotational motion?

MOI is a measure of an object's resistance to rotational motion. The higher the MOI, the more difficult it is to rotate the object. This is similar to how mass affects an object's resistance to linear motion.

How does the distribution of mass affect an object's MOI?

The distribution of mass greatly affects an object's MOI. Objects with a larger concentration of mass closer to the axis of rotation have a lower MOI, making them easier to rotate. Conversely, objects with a larger concentration of mass farther away from the axis of rotation have a higher MOI, making them more difficult to rotate.

What are some real-world examples of the application of MOI?

MOI is important in many real-world applications, such as designing vehicles, sports equipment, and machinery that require rotational motion. For example, engineers must consider MOI when designing a car's wheels to ensure they can rotate smoothly and efficiently. In sports, MOI is crucial in designing golf clubs, tennis rackets, and other equipment to optimize performance. It is also important in the design of industrial machinery, such as turbines and motors.

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