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AravindG

  • 4 years ago

A disc of radius r at time t=0 moving along positive x axis with linear speed v and angular speed w .Find the x and y coordinates of the bottommost point at any time t

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  1. JamesJ
    • 4 years ago
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    So is this point fixed, or is it the point that is always in contact with the surface? If it's the latter, it's trivial. So I'm guessing you actually want to first?

  2. AravindG
    • 4 years ago
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    hmm

  3. AravindG
    • 4 years ago
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    i hav a fig hope it helps

  4. AravindG
    • 4 years ago
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    |dw:1327765174049:dw|

  5. TuringTest
    • 4 years ago
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    |dw:1327764644850:dw|\[\overrightarrow{OP}=\overrightarrow{OA}+\overrightarrow{AB}+\overrightarrow{BP}=<r\theta,0>+\]

  6. anonymous
    • 4 years ago
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    |dw:1327765593766:dw|here dont bother about omega as as it is zero (v=rw) so just consider the velocity and plot down the points(for that u have to know how it moves along the axis at a given time ) considering uniform velocity v at time t in a straight line(x-axis) v/t will give the x-co-ordinate y co-rdinate is zero

  7. AravindG
    • 4 years ago
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    |dw:1327765734194:dw|

  8. AravindG
    • 4 years ago
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    is that the answr?

  9. AravindG
    • 4 years ago
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    hw is omega equal to 0??

  10. TuringTest
    • 4 years ago
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    \[\overrightarrow{OP}=\overrightarrow{OA}+\overrightarrow{AB}+\overrightarrow{BP}=<r\theta,0>+<0,r>+<-r\sin\theta,-r\cos\theta>\]\[\overrightarrow{OP}=<r\theta-r\sin\theta,r-r\cos\theta>\]subbing in omega t for the angle\[\overrightarrow{OP}=<r(\omega t-\sin(\omega t)),r(1-\cos(\omega t))>\]if we are talking about the situation I am imagining...

  11. JamesJ
    • 4 years ago
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    Nicely done TT

  12. TuringTest
    • 4 years ago
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    Thanks, hats of to OCW on that :D

  13. AravindG
    • 4 years ago
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    heyy TT why is your and salini's answr different?

  14. TuringTest
    • 4 years ago
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    I don't know what situation salini is imagining, but it is different than mine. I think he is imagining just looking at whatever point is on the bottom, not letting it rotate.

  15. AravindG
    • 4 years ago
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    so which is the right method?

  16. TuringTest
    • 4 years ago
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    if you are talking about this http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-c-parametric-equations-for-curves/session-17-general-parametric-equations-the-cycloid/MIT18_02SC_s17_applet.html then mine is right depends on what your question means, are we following point P or always looking at the bottom

  17. anonymous
    • 4 years ago
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    i thought that the point on the bottom lies on the axis of rotation of the disc then omega=v/r where r is 0

  18. AravindG
    • 4 years ago
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    look at my fig

  19. TuringTest
    • 4 years ago
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    Well which is it arvind? are we always looking at the bottom point or are we following point P which starts at the bottom?

  20. AravindG
    • 4 years ago
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    wel i think we are looking at co ordinates of bottom point

  21. AravindG
    • 4 years ago
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    but in pure rollindg dont we assume that the particles rotate about the bottom point???

  22. TuringTest
    • 4 years ago
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    then why does it ask for the y-coordinates if they don't change?

  23. AravindG
    • 4 years ago
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    hmmm

  24. anonymous
    • 4 years ago
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    oh i get it......when u said ocw helped u solve this was it walter lewin professors video?

  25. AravindG
    • 4 years ago
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    guys i will be back in 10 min

  26. TuringTest
    • 4 years ago
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    actually I learned about cycloids from the multivariable calculus section

  27. anonymous
    • 4 years ago
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    oh thank u for rresponding

  28. AravindG
    • 4 years ago
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    so wat is the answer is it salini's or turings??

  29. TuringTest
    • 4 years ago
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    ohj here it is http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-c-parametric-equations-for-curves/session-18-point-cusp-on-cycloid/ @arvind you have to figure out what your question is asking

  30. JamesJ
    • 4 years ago
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    ^^ exactly. The fact that you (Aravind) aren't clear on what the question is makes me very suspicious that you're actually paying attention to the method in the solutions. That is why I recommend again that you only post one or at the most two questions at a time. With those one or two questions, really, truly, thoroughly, completely understand the answers, then move onto the next problem. This is example number #9 or #10 in my book where it's clear to me you're not really paying attention to the answers we give. I'm not going to help you again, unless I see you try and really work out a problem with us, instead of putting things out there and grabbing in a half-*ssed way the answers and questions we propose back to you.

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