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Homework Help: Circular motion question

  1. Nov 10, 2005 #1
    This is the question...

    A small wheel of radius 1.4cm drives a large wheel of radius 15cm by having their circumferences pressed together. If the small wheel turns at 407 rad/s, how fast does the larger one turn? Answer in rad/s

    This is what I was thinking...

    radius of smaller wheel = .014m
    radius of larger wheel = .15m

    circumference of smaller wheel = 2*pi*r = 2*3.14*.014 = .08792
    angular velocity of smaller wheel (given) = 407 rad/s

    angular velocity = circumference/time
    time = circumference/angular velocity
    =.08792/407 = .000216s

    circumference of larger wheel = 2*pi*r = 2*3.14*.15 = .942

    angular velocity = circumference/time
    =.942/.000216 = 4361.11 rad/s

    Does this approach look right?
  2. jcsd
  3. Nov 10, 2005 #2
    I disagree... By intuition, you can predict that the larger wheel is going to turn more slowly.. Try another approach..

    Hint: Consider the fact that the speeds of circumferences are equal.

    Eq: speed = w x r

    w = angular velocity
    r = radius

    Does this help?

    Last edited: Nov 10, 2005
  4. Nov 10, 2005 #3
    You are right... the larger wheel should go slower.

    but since the speed of smaller wheel is 407 rad/s wont the larger wheel speed be the same?

    so is the answer to the problem 407 rad/s for the larger wheel? but that doesnt make sense because the larger wheel is supposed to go slower...

    I am confused...
  5. Nov 10, 2005 #4
    OK, so if the speed at the circumfrence is:

    v = w x r (as I stated above).

    If the wheels are in contact this speed is equal on both wheels (not the angular velocity). Therefore:

    wsmall x rsmall = wlarge x rlarge

    I can't give you anymore hints without doing it now.

    Good Luck... Let me know what you get for an answer.
    Last edited: Nov 10, 2005
  6. Nov 10, 2005 #5
    ohh i got it. i was confused between angular velocity (w) and tangential velocity(v).

    Hey another question. do you know if i did the right thing by converting the radius to (m) or should i have left it as (cm)?
  7. Nov 10, 2005 #6
    You could have left it as cm because you're dividing by the other length (which should have the same units).

    I usually convert thing to metres at the start though, its good practice in my experience.

    What was your final answer?

  8. Nov 10, 2005 #7
    ok thanks

    my final answer was 37.9866 rad/s

    does that sound about right?
  9. Nov 10, 2005 #8
    :smile: Exactly what I got
  10. Nov 10, 2005 #9
    thanks for all your help
  11. Nov 10, 2005 #10

    Glad to help. I joined this forum to get help, but giving help is just as useful to me, boosts my understanding too.
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