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'...
this counter is different..maybe only unique hits count!
ReplyDelete8R...!!!!!!!
ReplyDeletewell its getting interesting...:)
i am pretty much sure about this one!
accha...you wer able to get the scene without the diagram...cool!!!
ReplyDeleteman i just loved this one!!
ReplyDeletesame here 8R
ReplyDeleteplease tell how u did?
ReplyDeletevisualize this situation at the instant when the lowermost point is making an angle Q with the negative Y axis
ReplyDeletenow 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...:)