Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How is this length R(Theta)? I don't see it...

  1. Dec 16, 2015 #1
    ?temp_hash=66cabd9882823a10f05c3cfc502cfb5c.png

    That's the image. I can't see how the edge of that middle triangle's length is Rθ at all. I've tried using similar triangles and law of cosines to figure that out but I'm missing lengths. I thought Rθ was the arc length of a piece of a circle? So if Rθ is a length of a piece of a circle, how is Rθ equal to that edge of the triangle?
     

    Attached Files:

  2. jcsd
  3. Dec 16, 2015 #2
    It looks to me like this is a "given." You might be seeing right angles where none exist.
     
  4. Dec 18, 2015 #3

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Took me a few moments to figure it out. The answer is that the block started off horizontal then rocks to the left without slipping on the cylinder ... so the red and green lines in this version must be the same length...

    Figure.png
     
  5. Dec 18, 2015 #4
    But your green line doesn't equal R*theta as labeled, right?
     
  6. Dec 18, 2015 #5
    I.e., the extension of the radius R to the mid-point line of the bar is not parallel to the line from the top of the cylinder to the big black dot.
     
  7. Dec 19, 2015 #6

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Why not?
     
  8. Dec 19, 2015 #7

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    I had another think about this. I think you are right. I think the bit in yellow should have been omitted.

    Figure.png

    It becomes obvious something is wrong when theta is 90 degrees.
     
  9. Dec 19, 2015 #8
    Bingo; that was my "aha" moment also.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook