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Simple math question for physic problem

  1. Jan 3, 2013 #1
    Sans titre.png

    How do they get from the Rsinθ the value I have found the one I search: Rθ (extra string length)

    I know that sinθ = θ when θ is small but there Rsinθ is the extra height the mass gain when we push it from initial position to a θ angle with vertical, I don't see how it could be the extra string length.

    Thank you
     
  2. jcsd
  3. Jan 3, 2013 #2

    TSny

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    Hi, Dragster. It would be very helpful if you could describe the physical setup. I think I see what some of the expressions in the figure represent. But I don't understand at all what the small circle with diameter ##R\phi## represents. Is that some physical object?
     
  4. Jan 3, 2013 #3

    Curious3141

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    Like TSny, I don't get the exact physical setup. But I can tell you that the arc length (length along the curve of the circumference) subtended by an angle ##\phi## along a circle of radius ##R## is ##R\phi##. Does that help in relating the "extra string length" to that expression?
     
  5. Jan 3, 2013 #4
    I added the black circle with the ''?" on the top right.

    Do you mind if I can get the rigorous explanation why the arc is Rθ? Thank you for the fast answers

    Oh yea and for the problem, the string is attached on a cylinder. At theta = 0 with the vertical, the length is l0 and the asked result is the potential energy expression if the mass is pushed with an angle theta. I was only blocking on the part where I needed to know what was the extra string length.
     
  6. Jan 3, 2013 #5

    cepheid

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    It's from the definition of how angles are measured:

    http://en.wikipedia.org/wiki/Radian
     
  7. Jan 3, 2013 #6

    haruspex

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    When the string is vertical, the 'extra' string is wrapped against the cylinder and subtends angle phi at the centre. Clearly the angle subtended by an arc of a circle at its centre is proportional to the length of the arc, and the radian is defined in such a way that the length is simply radius * angle.
     
  8. Jan 4, 2013 #7
    Oh well I am really stupid after all.
    Thank you cepheid et harusphex :)
    First university session makes me feel like a complete ignorant idiot.
     
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