USAPhO 2026, Първи кръг — Задача 20
2026 Exam · 1 т.
Указания
25 QUESTIONS - 75 MINUTES
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
- Use throughout, unless otherwise specified.
- You may write in this question booklet and the scratch paper provided by the proctor.
- This test has 25 multiple choice questions. Select the best response to each question, and use a No.2 pencil to completely fill the box corresponding to your choice. If you change an answer, completely erase the previous mark. Only use the boxes numbered 1 through 25 on the answer sheet.
- All questions are equally weighted, but are not necessarily equally difficult.
- You will receive one point for each correct answer, and zero points for each incorrect or blank answer. There is no additional penalty for incorrect answers.
- You may use a hand-held calculator. Its memory must be cleared of data and programs. You may use only the basic functions found on a simple scientific calculator. Calculators may not be shared. Cell phones may not be used during the exam or while the exam papers are present. You may not use any external references, such as books or formula sheets.
- The question booklet, answer sheet and scratch paper will be collected at the end of this exam.
- To maintain exam security, do not communicate any information about the questions or their solutions until after February 13, 2026.
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
We acknowledge The US Physics Team coaches and other contributors to this year’s exams:
Tengiz Bibilashvili, Eddie Chen, Orhun Ciftcioglu, Kellan Colburn, Evan Erickson, Harry Kroft, Natalie LeBaron, Mai Qi, Elena Yudovina
Условие
Two uniform rigid rods lie in a vertical plane. The lower rod rests on a rough horizontal table at a single point and makes angle with the vertical. The rod can pivot about point without slipping.
The second rod is rigidly attached at its center of mass to the top of the lower rod at point . A motor causes the second rod to rotate in the plane about . The motor is rigidly attached to the lower rod and does not exert forces or torques on the table.
Which of the following types of motion of the second rod could keep the angle fixed in time?
(A) The second rod rotates with constant angular velocity
(B) The second rod rotates with angular velocity that varies periodically in time
(C) The system cannot remain at constant because only internal torques are produced by the motor
(D) The second rod rotates with angular velocity that increases linearly in time
(E) changes because the moment of inertia of the second rod about point varies during the motion
Отговори
- D
Решение
To keep the angle fixed, the gravitational torque about must be balanced by an opposite produced by the motor, which occurs via clockwise angular acceleration of the second rod. Since the second rod is connected at center of mass, the gravitational torque is independent of the second rod’s orientation, so should be constant, thus we require constant angular acceleration (D). Constant angular velocity would produce zero . The varying moment of inertia of the second rod about is not relevant.
Оригинал в Архива: 2026_FMA_exam.pdf · официални решения: 2026_FMA_solutions.pdf