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![[Post New]](/templates/default/images/icon_minipost_new.gif) 23 Feb 2008 23:58:04 IST
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Q. A circular disc of radius R is rolling on a horizontal surface. Find the distance travelled by a point P lying on the circumference of the cirle in one complete rotation.
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23 Feb 2008 23:59:18 IST
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wont it be 2 pi R for one complete rotation?
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24 Feb 2008 00:03:33 IST
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Well I think the point has travelled a distance 2piR wrt the disc. And the disc has moved a distance 2piR at the same time. So total distance travelled by the point is 4piR
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24 Feb 2008 00:06:39 IST
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The answer is 8R
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24 Feb 2008 00:08:04 IST
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| |  The cycloid is the locus of a point on the rim of a circle of radius  rolling along a straight line. It was studied and named by Galileo |
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" Always remember money isn't everything but make sure you have made a lot of it before talking such nonsense!"
- Bill Gates |
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24 Feb 2008 00:08:24 IST
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u mean this?
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" Always remember money isn't everything but make sure you have made a lot of it before talking such nonsense!"
- Bill Gates |
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24 Feb 2008 00:10:08 IST
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Yes it will be a cycloid but how do u find its circumference?
PS: I just gave a random shot in my previous answer. I am sorry.
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Let us learn to dream, gentlemen, and then perhaps we shall learn the truth.
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24 Feb 2008 00:10:55 IST
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Yes,the answer is 8R.But how???
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24 Feb 2008 00:11:47 IST
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Cycloid A cycloid is the curve traced out by a point on the circumference of a circle when the circle rolls along a straight line in its own plane. The equations of a cycloid created by a circle of radius 1 are x(t) = t - sin t y(t) = 1 - cos t Calculate the arc length S of the cycloid for 0  t  / 2.  Calculate the arc length S of the cycloid for 0 t / 2. this is what i got from net |
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24 Feb 2008 12:12:57 IST
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The speed of a point on the circumference of the disc is 2R sin t/2
integrate from t=0 to t=2 /.
You get 8R
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