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?