conservation of angular momentum - 2024 ACF Fall

Question

Answer the following about the study of falling cats, for 10 points each.

[10h] The study of falling cats began since treating cats as a single rigid body means the cat-righting reflex is a violation of this law. This law holds when the partial derivative of the Lagrangian with respect to theta is zero.

ANSWER: conservation of angular momentum [accept angular momentum is conserved; prompt on conservation; prompt on Kepler’s second law; reject “conservation of momentum”; reject “conservation of linear momentum”]

[10m] In Kane and Scher’s solution to the problem, cats are modeled as two of these solids. Radial, azimuthal, and height coordinates make up this 3 dimensional shape’s coordinate system.

ANSWER: cylinders [accept cylindrical coordinates]

[10e] To control the speed of their rotation, falling cats extend and retract their legs, which changes their value for this quantity. It is the angular analogue of mass.

ANSWER: moment of inertia [or rotational inertia; prompt on I; reject inertia]

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Summary


2024 ACF Fall at Claremont Colleges	fall	Y	4	22.50	75%	100%	50%
2024 ACF Fall at Cornell	fall	Y	9	13.33	100%	11%	22%
2024 ACF Fall at Illinois	fall	Y	9	16.67	100%	33%	33%
2024 ACF Fall at Rutgers	fall	Y	7	12.86	86%	14%	29%
2024 ACF Fall at Ohio State	fall	Y	8	13.75	75%	38%	25%
2024 ACF Fall at Georgia	fall	Y	10	15.00	100%	20%	30%
2024 ACF Fall at North Carolina	fall	Y	9	11.11	67%	33%	11%

Data


Claremont B	UCLA A	0	10	0	10
UCLA C	UCLA B	0	10	10	20
UCLA E	UCLA D	10	10	10	30
Claremont C	UCSD	10	10	10	30
Binghamton A	Cornell C	0	0	10	10
Cornell G	Binghamton C	0	10	10	20
Cornell D	RIT B	0	0	10	10
Syracuse	Cornell E	0	0	10	10
U of Rochester A	Cornell F	10	0	10	20
Cornell B	ESF	10	0	10	20
Penn State	Cornell A	0	0	10	10
RIT A	U of Rochester B	0	0	10	10
Binghamton B	RIT C	0	0	10	10
Chicago A	Illinois D	0	0	10	10
Northwestern A	Chicago B	0	0	10	10
Illinois A	Iowa B	10	0	10	20
Northwestern B	Iowa A	0	10	10	20
Illinois B	Notre Dame A	0	10	10	20
Illinois C	Purdue A	0	0	10	10
WashU A	SIUE	10	0	10	20
Notre Dame C	WashU B	0	0	10	10
Purdue B	Indiana	10	10	10	30
Columbia A	Columbia B	0	0	10	10
Penn A	Fordham A	0	0	10	10
Maryland B	Lehigh B	10	10	10	30
NYU A	Maryland A	0	0	10	10
Penn B	Rutgers A	10	0	10	20
NYU B	Princeton A	0	0	10	10
Rowan A	Rutgers B	0	0	0	0
CWRU A	Miami C	0	0	10	10
CWRU B	Michigan D	0	0	10	10
Michigan State A	Miami B	0	10	10	20
Michigan C	Michigan State B	10	0	10	20
Ohio State A	Miami A	10	0	10	20
Michigan A	Ohio State C	0	10	10	20
Jefferson County Scholars	West Virginia A	0	0	0	0
West Virginia B	Michigan B	0	10	0	10
Auburn A	Belmont	0	0	10	10
Clemson B	Emory A	10	0	10	20
Georgia Tech A	Georgia Tech B	10	0	10	20
Alabama A	Georgia Tech D	0	0	10	10
Clemson A	Georgia Tech E	0	10	10	20
Mississippi State A	Georgia A	0	0	10	10
South Carolina A	Georgia Tech C	10	10	10	30
South Carolina B	Auburn B	0	0	10	10
Vanderbilt A	Southern	0	0	10	10
Tennessee A	Vanderbilt B	0	0	10	10
Virginia Tech B	Appalachian State A	0	10	10	20
James Madison A	Duke B	0	0	0	0
Liberty B	James Madison B	0	10	10	20
UNC C	NC State	0	0	10	10
Liberty A	Tusculum	10	10	10	30
UNC D	UNC A	0	0	10	10
Virginia Tech A	UNC B	0	0	10	10
Duke A	Virginia	0	0	0	0
William & Mary	Appalachian State B	0	0	0	0