Finding the Center of Mass for a Uniform Plate

In summary, the conversation was about finding the x and y coordinates of the center of mass for a uniform plate with a given length. The solution involved setting up the plate as four rectangles and calculating the total moment of inertia using ML^2/12. It was also suggested to use L throughout the calculations to avoid mistakes.
  • #1
AnkhUNC
91
0

Homework Statement


What are (a) the x coordinate and (b) the y coordinate of the center of mass for the uniform plate shown in Fig. if L = 5.0 cm?

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c09/fig09_38.gif


Homework Equations





The Attempt at a Solution



So I think I should set this up as four different rectangles with a center particle mass. So this leads to Total = 110cm, xcom = ((20(10))+(30(-5))+(20(5))+(40(5))/110

Is this correct?
 
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  • #2
You must consider the plates as rectangular lamina and first calculate their individual moment of inertia using ML^2/12.
 
  • #3
AnkhUNC said:
Total = 110cm, xcom = ((20(10))+(30(-5))+(20(5))+(40(5))/110

Is this correct?

Hi Ankh! :smile:

First - common-sense - it's much easier if you use L throughout your calculations, and only put L = 5 right at the end - that way you're much less likely to make a mistake! :smile:

110 is correct.

hmm … you think I was kidding about mistakes? … try L^2 instead of L! :smile:
 

What is the center mass of a solid?

The center mass of a solid is the point at which the mass of the object is evenly distributed in all directions. It is also known as the center of gravity.

How is the center mass of a solid calculated?

The center mass of a solid can be calculated by finding the average of all the individual masses in the object, weighted by their distance from a reference point. This reference point is often chosen as the origin or the point of symmetry of the object.

Why is the center mass of a solid important?

The center mass of a solid is important because it helps us understand how an object will behave when subjected to external forces. It is also crucial in determining the stability and balance of an object.

Does the shape of a solid affect its center mass?

Yes, the shape of a solid does affect its center mass. Objects with irregular shapes or varying densities will have a different center mass compared to objects with uniform shapes and densities.

Can the center mass of a solid change?

Yes, the center mass of a solid can change if the mass distribution of the object changes. For example, if a solid object is cut into smaller pieces, the center mass will shift to accommodate the change in mass distribution.

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