Cycloid:



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The integration involved in the calculation of length of the involute was (after some thought), intuitive...there was little choice!!

Here's something better: the circular object rolls without slipping on a horizontal surface. The motion of the lowermost point 'P' is monitored.
The path traced by this point is called a 'cycloid'...again: find the length of the cycloid, assuming the radius of the circular body 'R'...

7 comments:

  1. this counter is different..maybe only unique hits count!

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  2. 8R...!!!!!!!
    well its getting interesting...:)

    i am pretty much sure about this one!

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  3. accha...you wer able to get the scene without the diagram...cool!!!

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  4. visualize this situation at the instant when the lowermost point is making an angle Q with the negative Y axis

    now let the CM move by a distance dx, the lowermost point moves about the arc by RdQ;
    take components
    the net displacement of the particle towards right is (dx-RdQcosQ) and the net vertical displacement is RdQsinQ
    also, dx=RdQ(remember rolling w/o slipping?)

    square and add to get the net distance, simplify, and integrate from 0 to 2pi...:)

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