2025 F=ma Review

Review of the 2025 F=ma Exam

The 2025 F=ma exam presented a diverse and challenging set of problems, staying true to its tradition of assessing students’ fundamental physics skills in classical mechanics. This year’s exam contained a mix of conceptual, algebraic, and problem-solving questions that required a deep understanding of kinematics, dynamics, energy, and rotational motion.

Notable Problems

1. Motion on a Plane (Problem 1)

   • This problem tested students’ ability to interpret graphical representations of motion. The given plots depicted position-time graphs in two dimensions, emphasizing the importance of understanding motion constraints when speed is constant but direction is not necessarily fixed. This problem rewarded students who had strong visualization skills in kinematics.

2. Elastic Collision of Disks (Problems 2 & 3)

   • These two problems were a highlight of the test, featuring a perfectly elastic collision between three identical disks on a frictionless surface. The simultaneous and sequential collision cases required students to apply both conservation of momentum and conservation of kinetic energy, providing a great test of collision theory and impulse concepts.

3. Cat and Mouse Chase (Problem 4)

   • This problem involved a cat chasing a mouse while maintaining a trajectory always pointed at the mouse. The result was an intriguing application of relative motion and acceleration in a non-inertial reference frame. Students had to recognize that the cat’s acceleration was dependent on its velocity relative to the mouse, making it a standout problem in the exam.

4. Three Cylinder Equilibrium (Problem 5)

   • This problem blended statics and friction, requiring students to determine when a system of three stacked cylinders remains in equilibrium. The inclusion of multiple coefficient of friction pairs made this question unique, as it tested both conceptual understanding and numerical computation skills in static equilibrium.

5. Rolling Ball Trajectory (Problem 6)

   • A classic mechanics problem with a twist, this question asked students to determine which starting position would result in the furthest horizontal landing point. The problem required knowledge of rotational energy, projectile motion, and the physics of rolling without slipping.

6. Walking Mechanism Energy Analysis (Problem 7)

   • Featuring a three-mass mechanism, this question required students to analyze the system’s total energy in terms of kinetic and potential energy components. The presence of a torsion spring added an extra layer of complexity, making it a great problem for students with a strong grasp of energy conservation.

7. Spinning Top on a Rotating Plate (Problem 8)

   • This problem introduced rotational reference frames by placing a spinning top on a counter-rotating plate. The relative motion analysis made this question particularly thought-provoking, requiring students to carefully consider angular velocity transformations.

8. Coupled Rotating Circles (Problem 9)

   • A standout conceptual problem, this question involved a nested system of rotating circles, where each subsequent circle’s center was fixed on the previous one. The question probed deep into rotational kinematics and acceleration periodicity, providing an exciting test of advanced mechanics.

9. Energy Transfer in Mass Collisions (Problems 10 & 11)

   • These two problems explored how kinetic energy is transferred between objects of very different masses in an elastic collision. Students had to derive and approximate maximum energy transfer fractions, reinforcing the principles of momentum and energy conservation in extreme mass ratio cases.

10. Tennis Ball Launcher and Rolling Motion (Problems 13 & 14)

    • This set of problems elegantly introduced rotational motion concepts, as students had to analyze how a slipping ball transitions into rolling motion. The comparison between different types of balls added another layer of depth to the question, requiring an understanding of moments of inertia.

Overall Difficulty and Impression

The 2025 F=ma exam maintained a well-balanced difficulty curve, offering both fundamental and highly challenging problems. Several problems, such as the coupled rotating circles and the cat-and-mouse chase, were particularly unique and required creative thinking. The exam was an excellent test of core mechanics principles, requiring students to apply both straightforward and sophisticated problem-solving techniques.

Final Thoughts

This year’s exam was an engaging and fair assessment for students preparing for the USA Physics Olympiad (USAPhO). The combination of conceptual depth, algebraic rigor, and real-world physics applications made it a memorable experience for test-takers. The problems were innovative, and the inclusion of multi-step reasoning problems ensured that only those with a strong grasp of physics concepts could excel.

Overall, the 2025 F=ma exam was another successful iteration of this competition, continuing to challenge and inspire future physicists.