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Chasles’s (“shal’s”) theorem states that any displacement of one of these theoretical objects can be represented as a rotation plus a translation. For 10 points each:
[10m] Name these theoretical objects whose motion about a fixed point can be represented using Cayley–Klein parameters or quaternions.
ANSWER: rigid bodies [or rigid body]
[10e] When rigid body rotation is free of this quantity, the right sides of Euler’s (“OY-lurz”) equations are set to zero. This quantity is the cross product of force and the lever arm.
ANSWER: torque [prompt on tau]
[10h] Euler’s equations in vector form set this expression of L and omega, where L and omega are the angular momentum and angular velocity pseudovectors, respectively, equal to the applied torque. This expression of L and omega is derived using the relationship between time derivatives in the space and body frames.
ANSWER: L-dot plus omega cross L [or L-dot + ω × L or L-dot plus the cross product of omega and L; accept the time derivative of L (in the body frame) or dL/dT in place of “L-dot”; accept answers that flip the addition, such as omega cross L plus L-dot; reject answers that change the order of the cross product, such as “L-dot plus L cross omega”]
<Physics>

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Summary

2023 ACF Nationals04/22/2023Y2314.7896%44%9%

Data

Chicago CMinnesota A1010020
North Carolina ACornell B010010
Yale AChicago A1010020
Michigan AImperial A010010
Johns Hopkins AMinnesota B0101020
UC Berkeley AMIT A010010
Rutgers AMcGill A010010
Ohio State AWUSTL A1010020
Penn State APenn A0000
Claremont ASouth Carolina A010010
Toronto AColumbia A010010
Georgia Tech BVirginia A010010
Harvard ATexas A1010020
Iowa State AIllinois A010010
Columbia BNYU A010010
Indiana ANorthwestern A10101030
Vanderbilt ARutgers B010010
Stanford AFlorida A1010020
UC Berkeley BPurdue A010010
Cornell AGeorgia Tech A1010020
Yale BWUSTL B1010020
Brown AChicago B1010020
Duke AMaryland A1010020