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April 26

Different ways of calculating center of mass

All the methods should give the same result, but I'm getting different answers.[1] Also, I don't know how to use the line integral to finish the problem. Imagine Reason (talk) 00:27, 26 April 2018 (UTC)[reply]

Why would you use a line integral to calculate something for a solid?—Jasper Deng (talk) 04:06, 26 April 2018 (UTC)[reply]

This is a surface, so it should be possible. Anyway the other methods don't agree either. 134.74.251.209 (talk) 13:40, 26 April 2018 (UTC)[reply]

@Imagine Reason: Method 2 is correct.
As for method 1, the

{\overline {x}}

being an abscissa of a center of mass does not mean the masses below and above

{\overline {x}}

are equal. If it did, the center of mass would not exist for any configuration of two different point masses! --CiaPan (talk) 15:15, 26 April 2018 (UTC)[reply]

I see your point. So how would I check my answer? As for the line integral, I was trying to apply Pappus's_centroid_theorem. 161.185.160.75 (talk) 16:46, 26 April 2018 (UTC)[reply]

I'll post it shortly, but the answer I get for the surface area using Pappus's theorem is 0.09141, which is supposedly the correct answer, even though the normal method, integrate 2*pi*y over x from 0 to 0.2, results in a surface area of 0.08378. 161.185.161.23 (talk) 20:42, 26 April 2018 (UTC)[reply]

You might be interested in reading on the difference between mean and median. The center of mass is based on the mean, whereas a line dividing the object into two equal masses corresponds to the median. -- Meni Rosenfeld (talk) 22:44, 26 April 2018 (UTC)[reply]