Problem statementSolution video |

**DISCUSSION THREAD**

Any questions?? Ask/answer questions below in the discussion thread.

**DISCUSSION**

It is recommended that you use the moving reference frame kinematics equations relating the motions of A and B:

**v**_{A} = **v**_{B} + (**v**_{A/B})_{rel} + **ω** x **r**_{A/B
}**a**_{A} = **a**_{B} + (**a**_{A/B})_{rel} + **α** x **r**_{A/B} + 2**ω** x (**v**_{A/B})_{rel} + **ω** x (**ω** x **r**_{A/B})

Attaching the observer and the *xyz*-axes to bar ACD prescribes * ω* and

*to be the angular velocity and angular acceleration, respectively, of ACD. What do you use for the relative velocity and relative acceleration terms,*

**α***(*and

**v**_{A/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.

**a**_{A/B})_{rel}

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

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.

Good observation.

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?

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.

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.

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

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

nevermind

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?

Madeline: Yes, that is correct.

I solved it this way, but my v_A/B_rel is not negative in the j and my omega is positive as well.