Euler equations - 2025 ACF Fall

Question

In tensorial form, these equations can be written as “I omega-dot plus omega cross the quantity I times omega” equals tau. For 10 points each:

[10h] Name these equations that relate the three principal moments of inertia to components of the angular velocity, angular acceleration, and torque vectors.

ANSWER: Euler (“OY-ler”) equations [or Euler’s equations; reject “Euler-Lagrange equations”]

[10e] The Euler equations can be derived from the fact that torque equals the time derivative of this quantity. Physics teachers often tilt a spinning bicycle wheel to demonstrate the conservation of this quantity.

ANSWER: angular momentum [prompt on L; reject “momentum”]

[10m] The bicycle wheel in the demonstration acts like one of these devices that contain a rotor spinning in a constant direction. Gravity can exert an external torque on these devices, causing them to precess.

ANSWER: gyroscopes [accept gyroscopic precession; prompt on tops by asking, “what devices do they behave like?”]

<Editors, Physics>

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Summary


Northern California	Main	Y	4	20.00	100%	100%	0%
Southern California	Main	Y	7	17.14	100%	71%	0%
Eastern Canada (1)	Main	Y	5	20.00	100%	80%	20%
Eastern Canada (2)	Main	Y	7	14.29	86%	57%	0%
Florida	Main	Y	2	15.00	100%	50%	0%
Great Lakes	Main	Y	12	11.67	58%	58%	0%
Lower Mid-Atlantic	Main	Y	9	7.78	78%	0%	0%
Upper Mid-Atlantic	Main	Y	10	16.00	80%	70%	10%
Upper Mid-Atlantic	Main	Y	2	15.00	50%	100%	0%
Midwest	Main	Y	9	17.78	89%	78%	11%
North	Main	Y	4	17.50	100%	75%	0%
Northeast	Main	Y	11	16.36	91%	64%	9%
Pacific	Main	Y	8	13.75	88%	50%	0%
South Central	Main	Y	7	14.29	71%	71%	0%
Southeast	Main	Y	12	15.00	83%	58%	8%
UK (North)	UK	Y	5	18.00	80%	100%	0%
UK (South)	UK	Y	7	17.14	86%	71%	14%
Upstate NY	Main	Y	5	20.00	100%	100%	0%

Data


Berkeley Mighty Miner	Berkeley Archer Queen	0	10	10	20
Berkeley Boss Bandit	Stanford B	0	10	10	20
Berkeley Skeleton King	Berkeley Little Prince	0	10	10	20
UCSC	Stanford A	0	10	10	20
Claremont C	UC Irvine	0	10	0	10
UC Santa Barbara	UCLA C	0	10	10	20
USC B	UCLA A	0	10	10	20
UCLA B	Claremont B	0	10	10	20
UCLA D	Claremont A	0	10	10	20
UCSD A	UCSD B	0	10	0	10
UCLA E	USC A	0	10	10	20
McGill E	Carleton A	0	10	0	10
McGill C	McGill A	0	10	10	20
McGill B	Ottawa D	10	10	10	30
Ottawa B	Ottawa A	0	10	10	20
Carleton B	Ottawa C	0	10	10	20
Guelph A	Toronto E	0	0	10	10
McMaster C	Toronto F	0	10	10	20
CWRU A	CWRU B	0	10	10	20
Pittsburgh	Kentucky	0	0	0	0
Louisville B	Ohio State A	0	10	10	20
Michigan State D	Louisville C	0	0	0	0
Michigan A	Michigan B	0	10	10	20
Michigan C	CWRU D	0	10	10	20
CWRU C	Michigan D	0	10	10	20
Michigan State A	Louisville A	0	10	10	20
Michigan State B	Ohio State B	0	0	0	0
Louisville D	Ohio State C	0	0	0	0
Ohio State D	Michigan State C	0	10	10	20
WVU B	WVU A	0	0	0	0
Toronto A	Waterloo A	0	10	10	20
Toronto C	Toronto B	0	10	10	20
Toronto D	McMaster A	0	10	0	10
Toronto G	Waterloo B	0	10	0	10
McMaster B	Waterloo C	0	10	0	10
South Florida A	Florida Tech B	0	10	0	10
Florida A	UCF A	0	10	10	20
William & Mary A	NCSU A	0	10	0	10
NCSU B	Liberty B	0	10	0	10
Liberty C	Tusculum A	0	0	0	0
UNC A	Virginia Tech A	0	10	0	10
UNC B	UNC C	0	10	0	10
Virginia Tech B	Virginia A	0	10	0	10
UNC D	Virginia Tech C	0	10	0	10
JMU A	William & Mary B	0	10	0	10
William & Mary C	Liberty A	0	0	0	0
Lehigh A	Rutgers B	0	0	10	10
George Mason A	Maryland B	0	10	10	20
Columbia B	George Mason C	0	0	0	0
George Mason B	Johns Hopkins	0	10	10	20
NYU B	Lehigh B	0	10	10	20
Rutgers A	Maryland A	0	10	10	20
NYU A	Maryland C	0	10	0	10
Princeton	Columbia A	10	10	10	30
Vassar B	Rowan	0	10	10	20
NYU C	Rutgers C	0	10	10	20
Penn	Rutgers D	0	10	10	20
Vassar A	Stony Brook	0	0	0	0
WashU Grizzlers	Chicago A	0	10	10	20
Purdue A	Chicago B	0	10	10	20
Illinois Champaign	Iowa B	0	10	10	20
Illinois Orange	Indiana B	10	10	10	30
Illinois Canada	Purdue B	0	10	10	20
Purdue C	Iowa A	0	10	10	20
Rose-Hulman A	Purdue D	0	0	0	0
Indiana A	WashU Grolars	0	10	0	10
William Woods University A	Illinois Blue	0	10	10	20
Wisconsin B	Minnesota	0	10	10	20
St. Thomas	Macalester	0	10	10	20
Iowa State	Wisconsin A	0	10	10	20
Michigan Tech	Wisconsin C	0	10	0	10
Boston University B	Amherst B	0	10	0	10
Boston College A	Brandeis Mozart	0	10	10	20
Dartmouth A	Brown A	0	0	0	0
MIT A	Brown B	10	10	10	30
Harvard	Brandeis Beethoven	0	10	10	20
Amherst A	Tufts A	0	10	10	20
Vermont A	Tufts B	0	10	10	20
UConn A	Boston University A	0	10	0	10
Williams A	Vermont B	0	10	10	20
Dartmouth B	Williams B	0	10	10	20
Dartmouth C	Williams C	0	10	0	10
British Columbia B	Texas	0	10	10	20
Washington State	British Columbia C	0	10	10	20
Washington Steelhead	Washington Chinook	0	10	10	20
British Columbia A	Washington Coho	0	10	0	10
Washington Masu	Washington Pink	0	10	0	10
Tulsa B	Central Oklahoma B	0	10	10	20
Kansas State A	Kansas State B	0	10	10	20
Murray State College A	Murray State College B	0	10	0	10
Nebraska A	Nebraska B	0	10	10	20
Nebraska C	Oklahoma	0	10	10	20
Rose State	Harding	0	0	0	0
Central Oklahoma A	Tulsa A	0	0	10	10
Alabama A	Vanderbilt A	0	10	10	20
Auburn A	Tennessee Tech	0	10	0	10
Clemson A	Chipola College	10	10	10	30
Montevallo	Clemson B	0	0	10	10
Clemson C	Sewanne	0	0	0	0
Georgia A	Emory A	0	10	0	10
Georgia Tech B	Auburn B	0	10	10	20
Georgia Tech C	Georgia Tech A	0	10	0	10
Georgia Tech F	Georgia Tech E	0	10	0	10
Vanderbilt B	Mississippi State A	0	10	10	20
South Carolina A	Tennessee A	0	10	10	20
Georgia Tech D	Tennessee B	0	10	10	20
Durham B	Edinburgh B	0	10	10	20
Durham D	Edinburgh D	0	0	10	10
Edinburgh C	Durham A	0	10	10	20
Edinburgh A	Sheffield A	0	10	10	20
Sheffield B	Durham C	0	10	10	20
Washington Atlantic	Alberta A	0	10	10	20
Alberta B	Washington Chum	0	10	0	10
Arizona State A	Washington Sockeye	0	0	0	0
Southampton	Cambridge A	0	0	10	10
Binghamton C	Rochester	0	10	10	20
Cornell D	Cornell A	0	10	10	20
Binghamton B	Cornell C	0	10	10	20
RIT A	ESF	0	10	10	20
Cambridge D	Imperial A	10	10	10	30
Imperial B	Birmingham	0	10	10	20
Imperial C	Bristol	0	10	0	10
LSE	Warwick	0	10	10	20
Imperial D	Oxford	0	10	10	20
Cambridge C	Cambridge E	0	10	0	10
Binghamton A	RIT B	0	10	10	20