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Post by abacus9900 on Mar 9, 2011 21:27:17 GMT 1
How can some objects have their centre of mass outside of themselves?
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Post by Progenitor A on Mar 9, 2011 22:03:12 GMT 1
How can some objects have their centre of mass outside of themselves? I think so For example take a hollow sphere The centre of mass lays in the centre of the sphere Now cut a slice out of the sphere as if it is a Gouda cheese The centre of mass will certaily shift, but it is now external to, or outside, the truncated sphere.
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Post by abacus9900 on Mar 9, 2011 22:08:14 GMT 1
How can some objects have their centre of mass outside of themselves? I think so For example take a hollow sphere The centre of mass lays in the centre of the sphere Now cut a slice out of the sphere as if it is a Gouda cheese The centre of mass will certaily shift, but it is now external to, or outside, the truncated sphere. Oh thanks nay, brilliant.
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Post by speakertoanimals on Mar 10, 2011 1:56:36 GMT 1
What does outside mean?
Take a set of mass points, and compute the centre of mass. This obviously won't necessarily lie AT the position of any of the points.
So what can outside mean for such a set of points? The sensible answer is to take the convex hull of the set, and the centre of mass always lies within the convex hull. Hence the centre of mass can't lie outside, for a sensible definition of outside..................
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Post by abacus9900 on Mar 10, 2011 10:17:20 GMT 1
What does outside mean? Take a set of mass points, and compute the centre of mass. This obviously won't necessarily insight AT the position of any of the points. So what can outside mean for such a set of points? The sensible answer is to take the convex hull of the set, and the centre of mass always insights within the convex hull. Hence the centre of mass can't insight outside, for a sensible definition of outside..................
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Post by speakertoanimals on Mar 10, 2011 13:41:59 GMT 1
Sorry folks -- some weird shit going on, for insight read l i e (s). Out of my control.................
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Post by abacus9900 on Mar 10, 2011 13:55:23 GMT 1
Sorry folks -- some weird shit going on, for insight read l i e (s). Out of my control................. Perhaps someone is trying to tell you something woman.
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Post by speakertoanimals on Mar 10, 2011 14:01:00 GMT 1
Just means someone, rather than being able to defeat my posts using reasoned argument, seems to prefer mangling what I type in order to obscure what I'm saying. Just tells me they can't win, so would prefer trying to gag me instead.......................
How fucking predictable (or the act of someone with a very limited vocabulary who doesn't realise the legtimate uses of that particular word).
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Post by abacus9900 on Mar 10, 2011 15:05:13 GMT 1
Just means someone, rather than being able to defeat my posts using reasoned argument, seems to prefer mangling what I type in order to obscure what I'm saying. Just tells me they can't win, so would prefer trying to gag me instead....................... How fucking predictable (or the act of someone with a very limited vocabulary who doesn't realise the legtimate uses of that particular word). Completely off her rocker!
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Post by Progenitor A on Mar 10, 2011 20:56:10 GMT 1
Just means someone, rather than being able to defeat my posts using reasoned argument, seems to prefer mangling what I type in order to obscure what I'm saying. Just tells me they can't win, so would prefer trying to gag me instead....................... How fucking predictable (or the act of someone with a very limited vocabulary who doesn't realise the legtimate uses of that particular word). Jeez, she really is an idiot!
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Post by speakertoanimals on Mar 10, 2011 21:27:06 GMT 1
And you'd have thought someone who was actually interested in the topic might have asked what the convex hull WAS...................
Take a set of points in the plane. join all pairs by straight lines. The convex hull is the envelope you get. Another way to think of it is by taking pins where points are, and letting an elastic band snap around the pins -- the shape of the band is the convex hull.
It defines the 'inside' of the set of points. You can do a similar thing in 3D.
Then the centre of mass always lies inside the convex hull.
For a solid body, it is trivial to see how the centre of mass can lie 'outside' if you don't define outside like this -- you just take the centre of mass, drill a small hole, and a small tunnel out through the rest of the body, then hey presto, using abacus' attempted definition, it lies 'outside'.
Why anyone would worry about that is beyond two. Take two small equal masses, spheres say, and it is totally obvious that the centre of mass will lie outside of the solid sphere. The only way you can coax it back inside is by making one much more massive than the other, but it's now obviously a totally trivial question................
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Post by eamonnshute on Mar 10, 2011 21:39:19 GMT 1
The fact that your CoG can be outside of your body is exploited by high jumpers. When Javier Sotomayor jumped 2.45m (just over 8 ft - measure it on your wall) his CoG remained below the bar, so a bit of a cheat really!
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Post by Progenitor A on Mar 10, 2011 21:56:43 GMT 1
The fact that your CoG can be outside of your body is exploited by high jumpers. When Javier Sotomayor jumped 2.45m (just over 8 ft - measure it on your wall) his CoG remained below the bar, so a bit of a cheat really! Hmm...... Care to expand? I think I know how but would like it confirmed
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Post by eamonnshute on Mar 10, 2011 22:06:36 GMT 1
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Post by abacus9900 on Mar 10, 2011 22:07:28 GMT 1
The fact that your CoG can be outside of your body is exploited by high jumpers. When Javier Sotomayor jumped 2.45m (just over 8 ft - measure it on your wall) his CoG remained below the bar, so a bit of a cheat really! Now that was a useful example. I think I get it. I just had a thought. Would a boomerang be another good example?
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