Moment of inertia of an ellipse formula

In summary, the conversation is about verifying the formula for the moment of inertia of an ellipse about its centroidal axis. The formula given by the person is M*(a^2 + b^2)/4, while a webpage states the formula as Pi*a*(b^3)/4. However, the person clarifies that the webpage is referring to the area moment of inertia, not the mass moment of inertia. After further discussion, it is confirmed that the formula calculated by the person is correct.
  • #1
Vineeth T
31
0
hello!
I have to verify the formula of the moment of inertia of an ellipse about its' centroidal axis,
is it M*(a^2 + b^2)/4.This is the one I got by myself.
But in a webpage it was given as Pi*a*(b^3)/4.

NOTE: don't ask for the proof of what I did.Its' a bit longer.I just want to know whether its' correct or
not.
 
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  • #2
You are mixing things up. The Quantity given on the webpage is is the "Area moment of Intertia" not the mass moment of inertia. Read on the two quantities and then you will see what to do...
 
  • #3
Ok then what I found out was correct.
 

What is the moment of inertia of an ellipse formula?

The moment of inertia of an ellipse formula is a mathematical expression used to calculate the rotational inertia of an ellipse. It takes into account the shape, size, and mass distribution of the ellipse.

What is the significance of the moment of inertia of an ellipse formula?

The moment of inertia of an ellipse formula is important in understanding the behavior of rotating objects. It helps determine how much force is needed to change the rotation of an object and how fast it will accelerate when a torque is applied.

How is the moment of inertia of an ellipse formula derived?

The moment of inertia of an ellipse formula is derived using the parallel axis theorem, which states that the moment of inertia of an object can be calculated by adding the moment of inertia of its individual components. In the case of an ellipse, the formula is derived by dividing the ellipse into infinitesimally small sections and summing up their individual moments of inertia.

What factors affect the moment of inertia of an ellipse?

The moment of inertia of an ellipse is affected by its mass, the distance of its mass from the axis of rotation, and the shape of the ellipse. A larger mass or a larger distance from the axis of rotation will result in a higher moment of inertia, while a more elongated shape will result in a lower moment of inertia.

How is the moment of inertia of an ellipse formula used in real-world applications?

The moment of inertia of an ellipse formula is used in various engineering and physics applications, such as designing rotating machinery, predicting the behavior of objects in orbit, and calculating the stability of structures. It is also used in sports, such as figure skating and gymnastics, to understand the movements and rotations of athletes.

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