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April 26

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Different ways of calculating center of mass

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