Introduction to the F=ma

 

What is the F=ma?

The F=ma is a contest organized by the Association of Physics Teachers (AAPT) that tests your problem solving skills within physics. The competition usually takes place at the start of the second week of February. Recently, the AAPT has changed the format of the competition so that there is only one version of the test you can take on one day.

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Out of the roughly 6000 people who take the F=ma exam, around 400 students qualify for the USAPhO, which is the second round of the competition that contains more challenging problems. A score of 14-18 is generally needed to qualify for the USAPhO. Of those 400 students, the top 20 people qualify for the training camp that occurs at the University of Maryland during the end of May. Five students out of the 20 students will be picked to represent the U.S. Physics Team in the IPhO (or in the case of 2024, the EUPhO). The IPhO is the pinnacle of physics competitions where 5 students representing each country around the world meet where the contest will be held.

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The test is intended for high schoolers. However, some middle schoolers also choose to take the test. The exam is proctored in the U.S. and the students taking the exam must be either U.S. Citizens, U.S. Permanent Residents (Green Card holders), or currently attending a U.S. school. 

 

What is the format of the competition?

The F=ma exam is composed of 25 questions that students are expected to answer in 75 minutes. All questions are equally weighted but vary in difficulty. Correct answers are awarded 1 point while incorrect answers are awarded 0 points. Since the AAPT does not penalize wrong answers, you should guess for all of the problems you don’t know. A handheld calculator with cleared memory may be used on the test but no other resources/aids are allowed.

 

What is tested in the competition?

The test focuses on classical algebra-based mechanics. The general breakdown of the exam is listed below.**

Kinematics (14.50%): vectors, kinematic equations, projectile motion, circular motion, and more

Dynamics (22.30%): statics, Newton’s laws, forces in mechanics, springs, frictional forces, and more

Energy (11.71%): kinetic energy, conservation of energy, work-energy theorem, energy dissipation, and more

Collisions (7.99%): conservation of linear momentum, elastic and inelastic collisions, ballistic pendulum, and more

System of Masses (5.20%): center of mass frame, pulleys with rotational inertia, and more

Rigid Bodies (11.34%): angular kinematic, moment of inertia, parallel-axis theorem, torque, rotational Newton’s 2nd law, rolling motion, and more

Oscillatory Motion (7.62%): SHM, simple and physical pendulums, mass-spring system, and more

Gravity (7.81%): gravitational force, Gauss’s law for gravity, binding energy, Kepler’s laws, circular and elliptical orbits, and more

Fluids (5.39%): Pascal’s law, buoyant force, continuity equations Bernoulli’s principle, Toricell’s law, surface tension, and more

Other (6.13%): dimensional analysis, error propagation, elasticities, waves, Young’s modulus, and more

 

Note that the subtopics presented within each topic are just general topics presented on the test and that many more theorems & techniques will come up. In recent years, error propagation has almost always (with 2024 as an exception) come up at least once. 

*Calculus is not needed on the test; however, it is advised that you still learn calculus-based physics.

**The percentages are based on tests from 2007 through 2023.

 

What can I do to prepare for the F=ma?

In short, it is crucial to read through an actual physics textbook, even if this may seem tedious at first. The textbook you read does not matter as physics content is the same in most textbooks. A recommendation for a beginner algebra-based physics textbook is Giancoli, Physics: Principles with Applications. An amazing book if you know calculus is Physics, Volume 1 by Halliday, Resnik, and Krane (commonly abbreviated as HRK). If available, also take AP physics as the curriculum coincides largely with the topics presented in the F=ma.

 

General tips!

• Learn calculus. Even though calculus technically is not required to qualify for the USAPhO, the subject can provide valuable insight into more difficult problems and enhance your knowledge of physics.

• Try solving actual F=ma problems! Solving past problems is a great way to test your understanding of the different topics. Practice problems are available in the link below: https://www.aapt.org/physicsteam/PT-exams.cfm

• Similarly, do the problems in the textbooks. This is imperative because merely learning the concepts will not be helpful unless you solve challenging problems alongside your readings. Many of the problems presented in the F=ma require deep insights that cannot be acquired by just knowing the general topics. Perhaps a good book with problems to prepare for the F=ma is Problems and Solutions in Introductory Mechanics by Morin.

• Don’t become stuck on learning one topic. Due to the myriad of different topics presented in the F=ma, it is crucial to rotate through different topics while studying.

• Have a good strategy for the exam. The difficulty of the problems in math contests such as the AMC 10/12 tends to become exponentially harder as the test progresses. However, the difficulty of the problems in the F=ma usually increases randomly and later problems can be much easier than earlier problems. 

• Lastly, remember to guess for all the problems you don’t know!

This article was written by our F=ma Expert, Jacob Lee.​