# Homework Help: Find the angular velocity of the Absolute Motion System

1. Mar 30, 2013

### Northbysouth

1. The problem statement, all variables and given/known data
Point A is given a constant acceleration a to the right starting from rest with x essentially zero. Determine the angular velocity w of link AB in terms of x and a.

I have attached an image of the question

2. Relevant equations

w = θ'

α = θ''

Pythagoras and trig

3. The attempt at a solution

x = 2bcos(θ)

x' = -2bθ'sin(θ)

x'' = -2bθ''sin(θ)-2bθ'2cos(θ)

a = -2bαsin(θ) - 2bw2cos(θ)

I know that bsin(θ) = √b2-x2/4

and I know that bcos(θ) = x/2

Substituting these is

a = -2α√b2-x2/4 - 2w2x/2

After here is where I get stuck. I'm not sure how to deal with the angular acceleration α. I can see that I have part of the final answer (shown in the image) but I'm not sure about the last few steps.

Any help would be appreciated. Thank you

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2. Mar 30, 2013

### TSny

Maybe you can get θ' from this. But you'll need to find x' in terms of x and a.

3. Mar 30, 2013

### Northbysouth

Looking at the problem again, I had thought that maybe I could use

x' = V0 + at

where V0 is zero, but this introduces another unknown. Am I over thinking this?

4. Mar 30, 2013

### Northbysouth

Ahh, wait. I got it. I was overthinking it. I only needed to take the first derivative. From there I can solve for θ'

θ' = -x'/2bsin(θ)

Knowing that a is constant I can use:

x' = v

v2 = v02 + 2ax

where v0 = 0

plug in √2ax for x'

Then i can also see that 2bcos(θ) = √4b2-x2

But I still have a negative in my final answer which shouldn't be there...

Last edited: Mar 30, 2013
5. Mar 30, 2013

### TSny

The signs are going to depend on your choice of positive directions. If you choose counterclockwise as positive $\omega$, then note that $\omega = -\dot{\theta}$.