Example of moment of inertia constant K, greater than one?

In summary, the moment of inertia constant, k, is a measure of the average distance of the mass of an object from its axis of rotation. It is often less than one and can be equal to one in certain cases, such as a bicycle wheel. An object with k = 1 would have all of its mass at a distance r from the axis of rotation, while a value of k > 1 would indicate that some mass is located at a distance greater than r from the axis of rotation.
  • #1
liometopum
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Regarding the moment of inertia constant, k, as in I = kmr^2, k is often a fraction less than one, and sometimes is equal to one. http://en.wikipedia.org/wiki/List_of_moments_of_inertia

Is there an example of k being greater than one?
 
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  • #2
The "k" is, in some sense, a measure of the average distance of the mass of an object from its axis of rotation. If all of the mass of the object is within radius r from the axis of rotation then the figure for k is guaranteed to be less than or equal to one.

The value of 1 is obtained when all of the mass is exactly at distance r from the axis of rotation. This would apply for something like a bicycle wheel where the mass is concentrated at the rim.

If you considered a thin square pipe rotating its long axis and if you measured its radius r from face to face (rather than from corner to corner) then I suppose that could give you a figure for k that is greater than one.
 
  • #3
What does an object with k = 1 look like? What would it mean for k > 1?
 

1. What is the significance of having a moment of inertia constant K greater than one?

The moment of inertia constant K is a measure of an object's resistance to rotational motion. When K is greater than one, it indicates that the object has a larger moment of inertia, meaning it will require more force to cause it to rotate. This can be useful in engineering applications where stability and control are important.

2. Can you give an example of an object with a moment of inertia constant K greater than one?

One example is a spinning top. The top has a large moment of inertia due to its shape and distribution of mass, making it difficult to change its rotational motion. This is why it can spin for a long time without falling over.

3. How is the moment of inertia constant K calculated?

K is calculated by taking the product of the mass of an object and the square of its distance from the axis of rotation. It is also dependent on the shape and distribution of mass of the object.

4. Does the moment of inertia constant K have any units?

Yes, K has units of mass times distance squared (kg•m2). This is because it is derived from the mass and distance measurements used in its calculation.

5. How does a moment of inertia constant K greater than one affect the stability of an object?

An object with a larger K value will have a greater resistance to rotational motion, making it more stable. This is because it will require more force to change its rotational motion, making it less likely to tip or fall over.

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