Unsolvable Angular Momentum Equation for Two Objects?

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Homework Statement



Diagram of two identical rods hanging vertically in a chain: rod AB pivots at fixed point A, rod BC hangs from B, with a horizontal impulse J applied at point D on BC, where BD is three-eighths of BC.


Homework Equations





The Attempt at a Solution


2 eqtns but 6 unknows, unsolvable?
Handwritten-style typeset derivation: Assume the motion of AB is independent of BC. Then P = dL_BC/dt and 0 = dL_AB/dt. Let initial angular speed of AB be ω_A and BC be ω_B. P = d/dt I(ω_Bf − ω_B) and 0 = d/dt I(ω_Af − ω_A), where ω_Bf and ω_Af are final angular speed.
 
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  • Handwritten-style derivation: Assume the motion of AB is independent of BC. Then P = dL_BC/dt and 0 = dL_AB/dt. Let the initial angular speed of AB be ω_A and BC be ω_B. P = d/dt I(ω_Bf − ω_B) and 0 = d/dt I(ω_Af − ω_A), where ω_Bf and ω_Af are final angular speeds.
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  • Diagram of two identical vertical rods AB and BC hanging from fixed point A, with B at the junction, a horizontal impulse J applied at point D on BC, and the problem statement text above it.
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