wizard85
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Angular velocity and vectors...
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].
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...
Homework Statement
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].
Homework Equations
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...
