Centroid 1

I was just working on a practical problem wherein i needed to calculate centroid of a curved wire.In my problem centroid happened to lie outside the wire.Can anyone tell if this is possible.If yes can you explain the reason physically?

 

[whymrg]

When you have a donut, centroid is located in the hole.

 

in my entry level days, some years ago!! when specifying reinforced concrete pipe dimensions, completely by mistake, I wrote down the number for outside diameter where I should have written down the inside diameter and the contractor, the genius that he was, made it so that the hole was outside the pipe!!
I thought I would sympthize with you!
Hey, its been a long day
good luck!

 

[trilinga]

The definition of a centroid is 'it is the point about which the first moment of the entity (length, area, volume or mass whichever is relevant to the context) is zero'. Physically, it is the point at which the whole mass (or length, area or volume as the case may be)of the body appears to be concentrated. In other words, it is the point at which the object will balance if supported with a single point support.

In your case, similar to many other shapes like 'L' or other open curves, the centroid or the point at which the body can be balanced with a single support lies outside the body. This is purely due to the shape of the body.

If one needs to support such an object through this point, the object needs to be externally connected to this point suitably before providing such a support. For the other objects with their CG lying inside them, such an arrangement is not needed.

 

Thanks, a million Trilinga!!!
But lets say we have an object say a book.Now, is it possible for the book to be stable if i support it with just one support may be even at the centroid of the book?

 

[trilinga]

Structurally it is very much true. The object will be in equillibrium. If the object is subjected to any other disturbances,(which normally occurs while supporting an object at a single point) the equillibrium may get disturbed.

I will put it a little diffrently for you to get the concept. The body will be in equillibrium under gravity load, if the resultant of the supporting forces ( may be one or more forces) passes through the centroid of the body. If the CG is outside the physical boundary of the body as the case you have come across, the supporting system shall be so defined to satisfy this condition to keep the body in equillibrium even under its own weight.

 

Thanks again Trilinga.