## 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

1. JamesJ

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

hmm

3. AravindG

i hav a fig hope it helps

4. AravindG

|dw:1327765174049:dw|

5. TuringTest

|dw:1327764644850:dw|$\overrightarrow{OP}=\overrightarrow{OA}+\overrightarrow{AB}+\overrightarrow{BP}=<r\theta,0>+$

6. anonymous

|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

|dw:1327765734194:dw|

8. AravindG

is that the answr?

9. AravindG

hw is omega equal to 0??

10. TuringTest

$\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

Nicely done TT

12. TuringTest

Thanks, hats of to OCW on that :D

13. AravindG

heyy TT why is your and salini's answr different?

14. TuringTest

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

so which is the right method?

16. TuringTest

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

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

look at my fig

19. TuringTest

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

wel i think we are looking at co ordinates of bottom point

21. AravindG

but in pure rollindg dont we assume that the particles rotate about the bottom point???

22. TuringTest

then why does it ask for the y-coordinates if they don't change?

23. AravindG

hmmm

24. anonymous

oh i get it......when u said ocw helped u solve this was it walter lewin professors video?

25. AravindG

guys i will be back in 10 min

26. TuringTest

actually I learned about cycloids from the multivariable calculus section

27. anonymous

oh thank u for rresponding

28. AravindG

so wat is the answer is it salini's or turings??

29. TuringTest

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

^^ 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.