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Homework Help: Angular velocity and vectors

  1. Feb 2, 2009 #1
    Angular velocity and vectors....

    1. The problem statement, all variables and given/known data

    Given the following vectors:

    [tex]\vec A=\hat i +\hat j - 2\hat k[/tex] and [tex]\vec C=\hat j - 5\hat k[/tex]

    Let [tex]\vec A[/tex] and [tex]\vec C[/tex] be drown from a common origin and let [tex]\vec C[/tex] rotate about [tex]\vec A[/tex] with angular velocity [tex]\vec w[/tex] of [tex]2 \frac{rad}{s}[/tex]. Find the velocity [tex]\vec v[/tex] of the head of [tex]\vec C[/tex].



    2. Relevant equations



    3. The attempt at a solution

    My step-by-step way for resolving it, is:

    1)I know that [tex]\vec v= w \times \vec C [/tex]
    2) By multiplying: [tex]\vec A \times \vec C [/tex] I'll find a vector parallel to [tex]\vec w[/tex] namely D
    3) Now, [tex]\vec D= \vec A\times \vec C=(\hat i +\hat j - 2\hat k) \times (\hat j - 5\hat k) = 7*\hat i -5*\hat j +\hat k [/tex]

    4) I also know that [tex]\vec w[/tex] is obtained by a linear combination of [tex]\vec D[/tex]'s parameter. Then:

    [tex]\vec w= a * \vec D=a * (7*\hat i -5*\hat j +\hat k)[/tex]

    but [tex]|\vec w|= 2 [/tex] so [tex] a= \frac{2}{|\vec D|}[/tex] --> [tex]a=\sqrt{75} [/tex]. Finally [tex]\vect w= \frac{2}{\sqrt{75}} (7*\hat i -5*\hat j +\hat k) [/tex]

    Thus:

    [tex] \vect v= \vect w \times \vect C = \frac{2}{\sqrt{75}} (7*\hat i -5*\hat j +\hat k) \times (\hat j - 5\hat k) [/tex]

    is that correct?

    Thanks to all... :smile:
     
  2. jcsd
  3. Feb 3, 2009 #2
    Re: Angular velocity and vectors....

    nobody? :frown:
     
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