How Do You Calculate the Velocity of a Rotating Vector?

[wizard85]

Angular velocity and vectors...

Homework Statement

Given the following vectors:

\vec A=\hat i +\hat j - 2\hat k and \vec C=\hat j - 5\hat k

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

Homework Equations

The Attempt at a Solution

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

1)I know that \vec v= w \times \vec C
2) By multiplying: \vec A \times \vec C I'll find a vector parallel to \vec w namely D
3) Now, \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

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

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

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

Thus:

\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)

is that correct?

Thanks to all...

 

[wizard85]

Homework Statement

Given the following vectors:

\vec A=\hat i +\hat j - 2\hat k and \vec C=\hat j - 5\hat k

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

Homework Equations

The Attempt at a Solution

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

1)I know that \vec v= w \times \vec C
2) By multiplying: \vec A \times \vec C I'll find a vector parallel to \vec w namely D
3) Now, \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

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

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

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

Thus:

\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)

is that correct?

Thanks to all...

nobody?