# Homework H3.B - Sp23

 Problem statement Solution video DISCUSSION It is recommended that you use the moving reference frame kinematics equations relating the motions of A and B:

vA = vB + (vA/B)rel + ω x rA/B
aA = aB + (aA/B)rel + α x rA/B + 2ω x (vA/B)rel + ω x (ω x rA/B)

Attaching the observer and the xyz-axes to bar ACD prescribes ω and α  to be the angular velocity and angular acceleration, respectively, of ACD. What do you use for the relative velocity and relative acceleration terms, (vA/B)rel  and (aA/B)rel ? Note that although B is a fixed point (zero velocity and zero acceleration), the observer on ACD sees B moving along the slot. The magnitudes of these relative velocity and acceleration terms are unknowns, however, the two vectors are aligned with the slot; that is, they have only y-components.

## 12 thoughts on “Homework H3.B - Sp23”

1. William Grant Dierking says:

I keep getting a (Vb/a)rel that is in the negative j when I do my calculations, but B appears to be moving upward from the perspective of A in the animation. Am I doing my calculations wrong, or is my understanding of what (Vb/a)rel incorrect?
Thank you

1. Benjamin Carl Wassgren says:

At the start of the animation (like in the conditions given by the problem) I think that B is moving down towards the moving reference frame. It only starts to move upward when the long section of the bar is close to perpendicular with the slope.

1. CMK says:

Good observation.

2. Benjamin Carl Wassgren says:

How are we supposed to find (vA/B)rel)? If we use the x and y components of the equation:
vA = vB + (vA/B)rel + ω x rA/B
we are left with 3 unknowns and 2 equations (ω, (vA/B)rel in the x direction, and (vA/B)rel in the y direction).
I don't think that the stationary reference frame helps at all since ω_AB != ω.
Is there something that I am missing here?

1. CMK says:

As xyz and the observer move with the L-shaped bar, the observer always sees B moving in the y-direction; that is, the x-component of (a_B/A)_rel is zero.

1. Benjamin Carl Wassgren says:

When I fully work out the problem using (vB/A)rel only in the y direction, I end up getting:
ω in the -k direction
(vB/A)rel in the -y direction
α in the -k direction
I think the values for (vB/A)rel and α make sense, but in the animation it looks like the reference frame is rotating in the +k direction (opposite the direction I calculated for ω) so I am unsure about my answers. I am confident in my math, so I am not sure if I have set up the problem wrong or if I have misread the animation.

1. Benjamin Carl Wassgren says:

never-mind, I had reversed the signs for the vector rB/A

3. eaub says:

Would the magnitude of aB/A be 0? Considering vA is constant, wouldn't vB/A also be constant?

1. eaub says:

nevermind

4. Madeline B says:

Since B is a fixed point, but the observer sees B moving, does that mean the v_B = 0, but v_A/B_rel is in the j?

1. CMK says:

1. Madeline B says: