As promised, here is another problem from our ALM110 major exam:

The diagram is self-descriptive. The 'hoop' rolls without slipping and its center moves to the right with a velocity 'V'. The radius of the hoop is 'R'.

Find the angular velocity of the rod.

Note: I have added a diagram describing the connection between the 'rod' and the 'hoop'.

18 comments:

  1. Sambhav GuptaDecember 1, 2010 at 5:34 AM

    is the rod tangent to the hoop?
    if yes, then answer is simply V/R

    ReplyDelete
  2. DeepakDecember 1, 2010 at 10:17 AM

    @Sambhav, the rod is not tangential... isn't that quite obvious?

    ReplyDelete
  3. AnujDecember 1, 2010 at 11:54 AM

    even if the rod were tangential, the answer would not have been v/r..

    ReplyDelete
  4. DeepakDecember 1, 2010 at 12:17 PM

    wait! the rod could not have been tangential in general... only an instant would occur when the rod would be tangential and yes even at that instant, velocity would not have been v/r

    ReplyDelete
  5. AnujDecember 1, 2010 at 12:44 PM

    Yess MyselfDeepakVasisht.

    ReplyDelete
  6. AmitDecember 1, 2010 at 4:03 PM

    I am getting v[cos(A) + sin(B)]/L

    ReplyDelete
  7. AnujDecember 1, 2010 at 11:24 PM

    answers anybody?

    ReplyDelete
  8. AmitDecember 1, 2010 at 11:41 PM

    bhaiya is my answer correct

    ReplyDelete
  9. AnujDecember 1, 2010 at 11:47 PM

    no, it is wrong.

    ReplyDelete
  10. AmitDecember 2, 2010 at 2:17 AM

    now I am getting v[cos(A)+sin(B-A)]/L, earlier did a calculation mistake, now it could be conceptual mistake.

    ReplyDelete
  11. Sambhav GuptaDecember 2, 2010 at 6:36 AM

    im getting a really long answer
    used sine rule to relate A, B, L and R

    took derivative to get another equation relating angular velocities and dL/dt

    i found dL/dt using geometry
    am i anywhere near the answer?

    ReplyDelete
  12. shouryaDecember 3, 2010 at 1:52 AM

    even i am getting v[cos(a)+sin(b-a)]/l.

    ReplyDelete
  13. AmitDecember 4, 2010 at 4:38 PM

    bhaiya please tell if it is correct..

    ReplyDelete
  14. AnujDecember 4, 2010 at 6:07 PM

    It is correct now.

    @Sambhav: you don't need to relate A,B,L and R.
    You are given these values. There may be a relation, but you need not consider it here.


    And, this is a fairly nice problem. You all can learn from it.

    And I had a thought. Bade Bhaiya taught Kullu Bhaiya, who taught Preyanshu Bhaiya, who taught me. All 4 have taught ECC 2012. 4 'generations' teaching a batch!!

    ReplyDelete
  15. Sambhav GuptaDecember 4, 2010 at 6:24 PM

    can anyone kindly tell me the solution?

    ReplyDelete
  16. AnujDecember 4, 2010 at 6:53 PM

    Let 'P' be the point of contact b/w the hoop and the rod.

    Consider 2 points:
    'P1' : on the rod.
    'P2' : on the hoop.

    These are the same as the point 'P', but on the different bodies.

    They (P1 and P2) should have the same velocity perpendicular to the rod.

    ReplyDelete
  17. Sambhav GuptaDecember 4, 2010 at 8:54 PM

    oh god....i COMPLETELY misunderstood this question, :|

    thank you bhaiya :)

    ReplyDelete
  18. PrashantDecember 5, 2010 at 12:37 AM

    nice thought bhaiya....come to anand vihar centre someday.....wud love to hear from you.....plzzzz :D

    ReplyDelete

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