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Damn analytical mechanics (2)

  1. Apr 2, 2005 #1
    Thanks for integral, he made the potential.pdf analyse for an analytical mechanic but i still have 2 questions,

    1- Why does the lenght up between the tengency point and top of (h) equals:

    [tex]\ell + r\theta[/tex] ?????????

    2- Why the kinetic energy here equals:

    [tex]T = \frac{1}{2} m(\ell + r\theta)^2 \dot{\theta}^2[/tex] ???

    I mean why we replaced R with [tex]\ell + r\theta[/tex] in the polar coordinates?



    Attached Files:

  2. jcsd
  3. Apr 2, 2005 #2


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    [itex]r \theta [/itex] is the arc length corresponding to the angle [itex]\theta[/itex] Notice that if you let [itex] \theta = 2 \pi [/itex] you get the circumference of the circle.

    As you unwind the rope moving the point of tangency through an angle [itex] \theta [/itex] you add the corresponding arc length ( [itex] r \theta[/itex] to the length of rope l which is initially hanging stright down.

    I need some time to look at the kinetic engery term. I concentrated on the potential energy term and have not looked into the kinetic energy. I'll get back to you, if no one else contributes.
    Last edited: Apr 2, 2005
  4. Apr 2, 2005 #3
    about the [tex]r\theta[/tex] i know it's the arc length (LOL I'm a second year university physics student), but the question is why does it equal to [tex]\ell + r\theta[/tex] in the tangent,

    I didn't understand integral, i'm very sorry, please explain it as a math geometric laws, And try using a simple language (I don't mean you language was complicated),

    And thanks very much
  5. Apr 5, 2005 #4
    Why no body is answeringgggg?????????????????
  6. Apr 5, 2005 #5


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    You say you are a second year university student. Did you ever learn to ride a bike? Do you remember the the first time you were given a push and told to pedal.

    There is nothing left in this problem which you should not be able to figure out on your own. Please study the diagram I drew for you and think about it. YOU CAN figure it out. Get 'er done
  7. Apr 6, 2005 #6
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