Angular Velocity Homework: Rigid Body Rotation w/ 3 rad/s

[4real4sure]

Homework Statement

Rigid body is rotating with 3 radians per second about an axis parallel to ax - 2ay + 2az. Express this mathematically.

Homework Equations

ax - 2ay + 2az

The Attempt at a Solution

w(vector)=w(1,-2,2) / 3 = (1,-2,2)
I need confirmation if this is correct or not. In either case, reasoning would be much appreciated.

 

[jedishrfu]

show you work and then we'll help.

 

[4real4sure]

The last statement itself was an attempt and I need "confirmation" if it is okay or not.

3. The Attempt at a Solution
w(vector)=w(1,-2,2) / 3 = (1,-2,2)
I need confirmation if this is correct or not. In either case, reasoning would be much appreciated.

 

[jedishrfu]

could you elaborate more on the ax - 2ay + 2az expression. Is this supposed to a vector as in ai -2aj +2ak where i,j,k are unit vectors? or is it the description of a plane where all points (x,y,z) reside on this plane ax - 2ay + 2az = constant ?

 

[vela]

could you elaborate more on the ax - 2ay + 2az expression. Is this supposed to a vector as in ai -2aj +2ak where i,j,k are unit vectors? or is it the description of a plane where all points (x,y,z) reside on this plane ax - 2ay + 2az = constant ?

Some books use the notation a_x, a_y, and a_z instead of i, j, and k for the Cartesian basis vectors.

3. The Attempt at a Solution
w(vector)=w(1,-2,2) / 3 = (1,-2,2)
I need confirmation if this is correct or not. In either case, reasoning would be much appreciated.

It would be correct if you had units on there. As far as the reasoning, you are supposed to supply that. Why do you think that's the way to solve this problem?

 

[4real4sure]

ax, ay, and az are unit vectors and I need to figure out the statement for the vector "w" which is in the attempt.

 

[4real4sure]

It would be correct if you had units on there.

I didn't get this

 

[vela]

Why don't you explain what you're doing?

 

[4real4sure]

Here it is, A rigid body rotates with angular velocity 3 rad/sec which remains stable. r is the distance vector from origin to a point Q, the position of a particle in the body. The velocity u of the body at Q is given by u = w X r (where u, w ,r are vectors). The rigid body is rotating parallel to ax — 2ay + 2az (where ax, ay, az are unit vectors) and passing through point (2, —3, 1), determine the velocity of the body at (1, 3,4).

Here I need to figure out vector u, vector r and vector w.
vector r=(1,3,4)-(2,-3,1)=(-1,6,3)
Now I need to find vector w for which I started out the question basically.

 

[vela]

I'm asking you to explain why you wrote

w(vector)=w(1,-2,2) / 3 = (1,-2,2)

Was this just some random combination of symbols? Is the 3 in the denominator because the angular speed is 3 rad/sec?