swing equation - 2026 ACF Regionals

Question

The left-hand side of this equation contains the inertia constant H, which quantifies the transient stability of a generator against frequency fluctuations. For 10 points each:

[10h] Name this second-order differential equation used to model synchronous generators which states that 2H over omega-sub-s times the second time-derivative of theta equals mechanical power.

ANSWER: swing equation

[10m] The swing equation is expressed in terms of either power or this other quantity that, for a motor, is plotted against RPM on a namesake curve. A car’s transmission is coupled to its engine by a “converter” of this quantity.

ANSWER: torque [accept torque curve; accept torque converter]

[10e] The swing equation is an application of the rotational version of this law, which states that torque equals moment of inertia times angular acceleration.

ANSWER: Newton’s second law of motion [prompt on Newton’s laws of motion or laws of motion; prompt on “F = ma”]

Back to bonuses

Summary


California (North)	Main Site	Y	3	16.67	100%	67%	0%
California (South)	Main Site	Y	4	10.00	75%	25%	0%
Canada	Main Site	Y	12	11.67	67%	50%	0%
Florida	Main Site	Y	3	6.67	33%	33%	0%
Great Lakes	Main Site	Y	4	17.50	100%	75%	0%
Midwest	Main Site	Y	8	13.75	75%	63%	0%
Overflow	Main Site	Y	4	12.50	75%	50%	0%
South Central	Main Site	Y	2	10.00	50%	50%	0%
Southeast	Main Site	Y	8	10.00	75%	25%	0%
UK	Main Site	Y	12	11.67	67%	50%	0%
Upper Mid-Atlantic	Main Site	Y	8	8.75	63%	25%	0%
Upstate NY	Main Site	Y	3	16.67	100%	67%	0%

Data


Berkeley A	Stanford B	10	10	20
Berkeley B	Berkeley C	10	10	20
Stanford A	Berkeley D	0	10	10
UCSD B	UC Santa Barbara	0	0	0
Simon Fraser	Brock	10	10	20
UBC B	Guelph	10	0	10
Carleton University	McGill A	0	0	0
McGill B	Toronto G	0	0	0
Ottawa	McMaster A	0	10	10
Toronto B	Waterloo A	10	10	20
Toronto E	Waterloo B	0	10	10
Toronto F	Western B	10	10	20
McMaster B	Toronto Metropolitan	0	0	0
UBC A	Queen's	10	10	20
Toronto D	Western A	10	10	20
Western C	Toronto C	0	10	10
Central Florida B	Central Florida A	0	0	0
Central Florida C	Florida A	0	10	10
Florida C	Florida B	10	0	10
Michigan C	CWRU A	10	10	20
CWRU B	Michigan State	10	10	20
Ohio State A	Michigan A	0	10	10
Pittsburgh	Michigan B	10	10	20
Northwestern B	Chicago A	0	0	0
Chicago B	Indiana C	10	10	20
Notre Dame A	Chicago C	0	10	10
Chicago D	Purdue A	10	10	20
Purdue B	Chicago E	10	0	10
Notre Dame B	Illinois B	0	10	10
Indiana A	Indiana B	10	10	20
Illinois A	Northwestern D	10	10	20
UC Irvine	UCSD C	0	10	10
UCLA A	UCLA B	10	10	20
UCSD A	Arizona State	0	10	10
Washington A	Carleton College	10	10	20
Alabama B	WashU B	0	10	10
Tennessee A	Georgia Tech B	0	10	10
Bruin	Georgia Tech C	0	0	0
Louisville B	Georgia Tech D	0	10	10
Louisville A	Kentucky	0	10	10
Mississipi State	Sewanee	0	10	10
Vanderbilt B	Tennessee B	10	0	10
WashU A	Alabama A	10	10	20
Minnesota A	Iowa State	10	10	20
Missouri B	Georgia Tech A	0	0	0
Murray State A	Texas A&M A	0	0	0
Texas A	Texas B	10	10	20
Claremont	Washington B	0	10	10
Bristol	Cambridge A	0	10	10
Cambridge C	Southampton B	0	10	10
Cardiff	City St. George's	0	10	10
Birmingham	Durham	10	10	20
Edinburgh A	Imperial A	10	10	20
Edinburgh B	Montpellier	10	0	10
LSE	Imperial B	0	0	0
Warwick B	Imperial C	10	0	10
Oxford A	Manchester	10	10	20
Oxford B	Oxford C	0	0	0
Southampton A	UCL	10	10	20
Warwick A	Cambridge B	0	10	10
Georgetown	Johns Hopkins B	0	0	0
Johns Hopkins A	NYU C	0	10	10
Maryland A	Swarthmore	0	10	10
Maryland B	Columbia C	0	10	10
NYU A	Vassar	0	0	0
Columbia A	NYU B	10	10	20
Columbia B	Rutgers A	0	10	10
Catholic	Rutgers B	10	0	10
Cornell C	Binghamton B	10	10	20
Penn State	Cornell B	0	10	10
RIT	Cornell A	10	10	20