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Working with a "rotating" pendulum

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This problem has caused alot of dificulty.
Both the ta and prof. have as yet not come up with a solution. A general concensus is that the higher circular path of the shortened length has a smaller diameter, unlike the picture.
A) L1^3 * sin^3 theta1 * tan theta1 = L2^3 * sin^3 theta2 * tan theta2
B) 49.8 degrees.
But how they are derived is as of yet unknown

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We have to take in to account the fact that the angular momentum is conserved in this case. To conserve angular momentum, the pendulum changes its angle or rotation if the length is changed.

Thus we will write, m1 v1 r1 = m2 v2 r2

Since mass is equal, ...

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