Doing physics problems in a systematic way

I appreciate very much that a number of you took the time to come to talk to me about your Test 3 performance. It is my pleasure to work with students on one-on-one basis. This allows me to see students' thought processes in setting up a problem, and in working out the details toward solving a problem. I have a piece of general advice, which I believe is applicable to, at least 50% of the students I have spoken to.Each of you should develop a systematic way of solving a physics problem (or individual parts of a problem). Below I am going to suggest a systematic approach for doing physics problems which may be useful in doing homework and in taking an exam. A student should feel free to modify the procedure outlined so that it is suitable for him/herself. Among other things, the student must take into account his/her strengths and . The approach may also vary to some extent depending on the nature and the level of individual problems involved.

During an exam you are given a number of blank sheets. Divide them into two categories. For definiteness, let me refer them as the "scratch pages" and the "work sheets". Similar division may also be desirable when doing your homework. Scratch pages are temporary "thinking pads". Any worthwhile information should be transferred your work sheet(s). The worksheet must have an organized layout. We suggest students only use one side of the worksheet. For each problem, it should begin with "givens" and "to finds" and the "sketch(es)", if ineeded. Problems on the worksheet should be properly separated. Whenever practical, avoid putting one problem on two worksheets. Label the pages of work sheets and problems on each page in an organized fashion.

1. Preliminary stage: Understand the question.

• Spend time to understand the question.
• Learn from the textbook, a set of "generic symbols" used in labelling various quantities. Use symbols as a short cut (e.g. often it is not necessary to write down the numerical values), to identity "the givens" and the "to find".
• Whenever applicable, sketch a diagram or diagrams and label them appropriately.
• Transfer all the key information for a given problem on to your worksheet. This so you feel comfortable in proceeding to work on the problem with a minimal reference to the original Problem Printout, if at all.
• When doing your homework, if you are not able to understand a question, you should go back to: textbook, lecture notes, and/or the IQ questions which concern materials on similar topics.

2. Logical reasoning: Write down the correct physics equation(s)

• With the help of the course summary sheet, identify the physics principles and formulas which may be applicable to this problem. Incidentally, over half the students who came to talked to me did not come with their course summary sheet. I encourage y'all to use the sheet as your study companion. It may help you to be more focused.
• Write down equations which correctly describe the "physics" of the present problem. From these equations, decide a strategy to solve the present problem. .

Take for example the problem of the Physical Pendulum in Test 3. A student told me that she wrote down [torque=I*alpha]. She then got confused as to what moment of inertia should one use. Should it be defined about the center of mass, i.e. I_cm, or should it be about the pivot point P, I_P?

To see what goes on, one must go back to the basics, to think about what might be the correct physics. In this problem the torque is pivoting about P. It rotates the meterstick. We may divide the meterstick into many elements. Denote the mass of the i_th element be m_i. It has a tangential acceleration a_i=r_i*alpha, where r_i is the distance from P to the ith element. One may also divide the total torque into matching parts, with each part rotating the corresponding element. Torque_i is responsible for rotating the element m_i. With a lever-arm r_i and the tangential force F_i=m_i*a_i, torque_i=r_i*(m_i*a_i)=(m_i*r_i**2)*alpha. I_P=sum(m_i*r_i**2). So we see the correct physics corresponds to having the moment of inertia evaluated about the pivot point, P. The key point we want to stress is that the correct physics should be directly correlated to the situation of the present problem.

3. Analysis and results.

• Work out your answer.
• If your calculation is lengthy, see if you can try to shorten the steps. Usually there should only be 2-3 key steps. You need to spend time to check the key steps carefully. For instance in my comments on " This course requires rigorous discipline " those factors of sine, cosine, the inverse power laws, the change of potential energies are the key steps where one must go over the factors at least two or three times to ensure the correctness of the answers. I often use the analogy that one seldom makes a mistake on the first digit in one's bank account, since it is very important to the person. Students in physics should develop sensitivities in identifying the key steps in a calculation. These are the crown jewels of a problem. They should be handled with a great care.
• It is advisable to go through these 2-3 key steps toward the end of the exam. Some students told me that they had the correct answer but later on when they checked the problem again they changed from the correct answer to the wrong answer. This is not always the case. Physics has its objective reality. You are pursuing truth. I believe when physics is understood properly, the more you check it better it looks. I like the quotation: "Thou shalt know the truth. And the truth shalt set thou free."
• Check your answers by doing intuitive reasoning:
  • Visualize whether your answer is physically sensible.
  • Do the "extreme situation analysis" (the actual situation should be somewhere in between the two extreme cases.
  • Check the dimensional agreement.
  • etc.

To sum up, I encourage you to develop and refine your approach in studying physics. I believe the improvement of study habits, which you pursue while taking this course, could also have an impact in your career. Please do come to see me if you need help.