Mass moment of solids

In summary, the conversation discusses the formulas for the static moments of a solid about the coordinate planes Oxy, Oyz, and Oxz, and how these relate to finding the center of mass and balancing a solid. The integral formulas give the average mass density weighted value of each coordinate, which determines the center of mass. The concept of "moment about a plane" refers to the solid's moment about multiple axes at the same time.
  • #1
Nikitin
735
27
http://www.math24.net/physical-applications-of-triple-integrals.html

"The static moments of the solid about the coordinate planes Oxy, Oyz, Oxz are given by the formulas"

What exactly does that mean? I understand what a moment about an axis is, but about a plane? what? Do they mean moment about two axis at the same time, or something?

And how did they arrive at the following formulas? http://www.math24.net/images/7tri2.gif [Broken]
 
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  • #2
Help?
 
  • #3
Nikitin said:
Help?

The integrals give you the average mass density weighted value of each coordinate.

One shows that these weighted coordinates determine the center of mass. For a rigid body, its kinematics can be reduced to the motion of its center of mass - I think.
 
  • #4
If a solid has a moment about a plane, what does this mean? I know that you can find the centre of mass in a solid, and then use this point to balance the solid, but how does this relate to "moment about plane"?

Does the "moment about the xy-plane" simply mean the solid's moment about the x and y axis?
 

1. What is mass moment of inertia?

Mass moment of inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is the rotational equivalent of mass in linear motion and is dependent on the distribution of mass in an object.

2. How is mass moment of inertia calculated?

The mass moment of inertia of a solid can be calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. This calculation can become more complex for irregularly shaped objects, where the mass must be divided into smaller elements and the individual moments of inertia must be summed together.

3. What is the significance of mass moment of inertia?

The mass moment of inertia is important in understanding the stability and balance of rotating objects. It also plays a critical role in determining the amount of torque required to accelerate a rotating object to a certain angular velocity.

4. How does the mass moment of inertia affect an object's motion?

Objects with a higher mass moment of inertia will have a greater resistance to changes in rotational motion and will require more torque to accelerate or decelerate. This is why objects with a larger radius, such as a spinning top, are able to maintain their rotational motion for longer periods of time.

5. How can the mass moment of inertia be altered?

The mass moment of inertia can be altered by changing the distribution of mass in an object. For example, by moving mass further away from the axis of rotation, the moment of inertia will increase. Additionally, the shape and orientation of an object can also affect its moment of inertia.

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