# Crane Problem, Finding Angular Velocity

1. Jul 21, 2010

### jiffy

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

At the instant shown in the figure , the crane's boom has an angle = 33.0 and rotates around the vertical axis with angular velocity = 8.00×10^−2 radians/s that increases at the rate = 7.00×10^−2 radians/s^2. At the same instant, the crane's boom is rotating upward with angular velocity = 3.00×10^−2 that increases at the rate = 5.00×10^−2 . Determine wx, wy, and wz, the i, j, and k components of w, the boom's angular velocity in the fixed reference frame X, Y, Z. The translating-rotating reference frame, x, y, z, lines up with the fixed reference frame at the instant shown.

> The figure shows a crane with the z-axis vertical and the y-axis along the cranes boom. The angular velocity are all rotating counterclockwise. The origin is at the center of the crane.

2. Relevant equations

vp = wp X rp

vp is the velocity at a point
w is the angular velocity
rp is the position of the vector at a point

3. The attempt at a solution

w = w1 * w2 = (.03i + .08k)rad/s
$$\Omega$$ = .08k rad/s
w = $$w_{12}$$ + $$\Omega$$ X w = (.05i + .07k) + .08k X (.03i + .08k)

=0.05i + 0.0024j + 0.07k

That was my final answer but it is wrong.

2. Jul 22, 2010

### 6Stang7

How are you taking the acceleration of the crane into account?

3. Jul 22, 2010

### jiffy

I'm taking into account the acceleration in my equation but the answer is still not correct:

w = + $$\Omega$$ X w = (.05i + .07k) + .08k X (.03i + .08k)