1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Determine the Angluar Velocity of the Slender Rod.

  1. Mar 30, 2013 #1
    1. The problem statement, all variables and given/known data
    Calculate the angular velocity w of the slender bar Ab as a function of the distance x and the constant angular velocity w0 of the drum.

    I have attached an image of the question

    2. Relevant equations



    3. The attempt at a solution

    x = √(x2+h2)cos(θ)

    x' = -√(x2+h2)sin(θ)θ'

    θ' = -x'/√(x2+h2)sin(θ)

    θ' = -x'/h

    But I'm not sure where to go from here. I'm having trouble dealing with x'.

    Any advice would be appreciated.
     

    Attached Files:

  2. jcsd
  3. Mar 30, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    When taking the time derivative, you neglected the time dependence of x on the right side of the equation. It will be easier if you start over and use a different trig function than cosine.
     
  4. Mar 30, 2013 #3
    Do you mean something like:

    x = h/tan(θ)
     
  5. Mar 30, 2013 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes. And 1/tanθ equals another trig function.
     
  6. Mar 30, 2013 #5
    Do you mean 1/tan(θ) = cos(θ)/sin(θ) ?
     
  7. Mar 30, 2013 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    No. cotθ
     
  8. Mar 30, 2013 #7
    With this information I've managed to get:

    x = h/tan(θ)

    x = hcot(θ)

    x' = -hcsc(θ)

    θ' = -x'/hcsc(θ)

    θ' = -x'sin2(θ)/h

    And I know that h = √(x2+h2)sin(θ)

    θ' = (-x'sin2(θ))/√(x2+h2)sin(θ)

    Which simplifies to:

    θ' = -x'sin(θ)/√x2+h2)

    I also recognized that sin(θ) = h/√(x2+h2)

    θ' = -x'h/(x2+h2)

    At this point I'm a little unsure of the x' and what to substitute it with. I know that:

    v = wXr = rwcos(θ)

    I'm unsure if what I've written here for v is correct. Particularly, as the given answer does not have a cos(θ) in it.

    Could someone clarify this for me?
     
  9. Mar 31, 2013 #8

    TSny

    User Avatar
    Homework Helper
    Gold Member

    x'= v = tangential speed of rim of drum = rω

    Note: from the equation θ' = -x'sin2(θ)/h it would be easier to substitute for sinθ rather than substitute for h.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted