Hello teachers and student, I have a doubt, how much distance a point on cirumference of a tyre travels during one complete roatation of tyre on road. pls dont sat 2pie*r, as this is the disctance travelled by centre,not point on circumference.

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What you have asked is a very good question. The kind of motion is called refers to the geometry of cycloid, and in such a case the distance traveled by the point is equal to 8r where r = radius of the circle. The calculation can be read from Wikipedia from the following link http://en.wikipedia.org/wiki/Cycloid#Evolute There...
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What you have asked is a very good question. The kind of motion is called refers to the geometry of cycloid, and in such a case the distance traveled by the point is equal to 8r where r = radius of the circle. The calculation can be read from Wikipedia from the following link http://en.wikipedia.org/wiki/Cycloid#Evolute There is a very nice animation showing the actual motion. Hope this helps. Cheers read less
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GMAT Math Expert

Suppose you take a point on circumference that is touched with ground, now on one complete rotation the same point will tough the ground again and for that it has to pass all over the circumference. So again circumference of a circle is 2*pie*r
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Maths and physics teacher till engineering level

Linearly both distances are same...
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The curve generated by a point on the circumference of a circle when the circle rotates on a straight line is called a cycloid. If 'r' is the radius of the generating circle then the arc length of this cycloid for one rotation of the circle is = 8r.
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Maths Teacher

When a tyre makes one complete revolution, it means that the centre remains stationary. Actually 2pie *r is the distance a ny point on the circumferance of the tyre trvels during one complete revolution. When a tyre makes a revolution it means that it revolves aroung its centre. Hence centre does not...
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When a tyre makes one complete revolution, it means that the centre remains stationary. Actually 2pie *r is the distance a ny point on the circumferance of the tyre trvels during one complete revolution. When a tyre makes a revolution it means that it revolves aroung its centre. Hence centre does not travel any distance. read less
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Headstart to assured 95+ score in math

Many thanks to Santosh sir. Many of us supposed that the displacement is being asked when it was the diatance which is asked. http://en.wikipedia.org/wiki/Cycloid#Evolute
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Teaching is my passion!!!!

It will be 2*pi*r. Any point on circumference will travel the same distance as centre but in circular and linear direction respectively..
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Linearly both distances are same.
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B.tech m.tech from nit with 20 yrs of teaching experience.

Obviously this distance is equal to circumference because if you cut the circle at a point and open it up then it is in the form of a straight line with length equal to circumference.
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B.Tech IIT Delhi, Madly in love with Science

The locus of a point on the circumference of a tyre is a curve known as cycloid. And the length of this curve for one rotation of the tyre is 8R, where R is the radius of the tyre. Thie Length can be calculated using the formula of the length of a curve in calculus. You will need the parametric equations(r...
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The locus of a point on the circumference of a tyre is a curve known as cycloid. And the length of this curve for one rotation of the tyre is 8R, where R is the radius of the tyre. Thie Length can be calculated using the formula of the length of a curve in calculus. You will need the parametric equations(r -theta form) of the cycloid. read less
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