Angular Vector Help: Solving Wheel & Turntable Problem

[WyldFyr]

OK, I usually like to work this stuff out on my own, or limp along. So, if i didn't think i was a little over my head, i wouldn'y be starting this thread.

I am aproaching a test that will include all the stuff on angular: velocity, acceleration, momentum, torque, and moments of inertia, that we are supposed to know. I got the basics of all those, but I'm still having trouble with using (and understanding) the vector concepts.

The trouble started with this homework problem, and this is where I'm working from to prepare for this test ( 3 days away, I'm not waiting to "the" last moment).

Problem: The Axle of a wheel is mounted on supports that rest on a rotating turntable (the axle is horizontal to the turntable). The wheel has angular velocity of 50.0 radians/sec. about its axle, and the turntable has angular velocity of 35.0 radians/sec. about a vertical axis. Take the z axis vertically upward, and the direction of the axle at the moment shown to be the x-axis pointing to the right.(the diagram shows the turntable rotating counter clockwise, and the wheel rotating away from view at the top)
- What is the angular velocity of the wheel as seen by an outside observer, at the instant shown?
- What is the magnitude and direction of the angular acceleration of the wheel at the moment shown?

For the first part I added the vectors for the two velocities together and got 61 radians along 35 degress in the plane of -x,z ( (-50i + 35k) rad/s ), which is correct according to the book. But i am still trying to grasp how to get the acceleration, and I'm not getting much help from proff. or book.
All I'm asking for is help in getting unstuck, so i can roll along again.

(edit) B.T.W. The acceleration is -1750j rad/s^2. I'm working backwards now to try and understand this.

 

[durt]

First find the angular velocity vector of the wheel in terms of the axle's displacement $$\theta$$ in the x-y plane (hint: trig). Then find it in terms of time $$t$$ (because you know the angular velocity of the turntable). Just be careful as to where you define $$\theta = 0$$ and $$t = 0$$. Then do some differentiation ($$\alpha = d \omega / d t$$) and you're good to go. (Plug in $$t=0$$).

 

[WyldFyr]

Rolling, Rolling, Rolling...
Thanks so much for your help. I've spent the last 36hours working, eating, sleeping, and trying to understand what you said. I think I have it now, and here it is for anyone else who reads this.


So, the axis of rotation(of the wheel) is also rotaing in the x-y plane. I can find the angle of the axis of rotation of the wheel with regards to the turntable by ω*t (ω is going to be the rotation of the turntable, because i still don't know how to do subscripts in this forum). Once I have this, i can create a function for the position of the wheel's rotational velocity vector; angle=ω*t, magnitude= -50 rad/s. In conponet form, this would look like: (-50 rad/s)*( Cos(ω*t)i + Sin(ω*t)j ) If i differentiate this (wrt t), i would get "change in velocity, with repect to time", aka acceleration!

The diiferentiated form looks like this:
(-50 rad/s) * ( -Sin(ω*t)*ωi + Cos(ω*t)*ωj) = α

Plugging in the values for ω= 35 rad/s and t=0, i get:
(-50 rad/s) * (-Sin(0)*(35 rad/s)i + Cos(0) *(35 rad/s)j)
which is (-50 rad/s)*(35 rad/s)j = (-1750 rad/s^2)j = α
... which is what the book says it should be! Woohoo!

Did I also get the concepts right?