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Consider a stick of mass M and length L, which is constrained to move such that it is always a chord of a fixed vertical, circular ring of radius R. For 10 points each:
[10m] The moment of inertia of the stick relative to the ring’s center can be calculated using this theorem, coming out to be M times the quantity R-squared minus one-sixth L squared.
ANSWER: parallel axis theorem [or Huygens-Steiner theorem; reject “perpendicular axis theorem”]
[10h] This quantity for the system equals “one-half I theta-dot squared, minus Mgd times the quantity one minus cosine theta,” where d is the distance from the center of the ring to the stick.
ANSWER: Lagrangian [prompt on L]
[10e] Solving the equation of motion for small perturbations about the equilibrium position shows the system exhibits this behavior. Systems obeying Hooke’s law display the “simple harmonic” form of this motion.
ANSWER: oscillation [accept simple harmonic oscillation or SHO]
<BW, Physics>

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Georgia Tech AMississippi State1001020
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