This course requires rigorous discipline

Yesterday a student came to see me. He did not do well on Test 3. We went through some of his mistakes and explored ways which might help him to improve his future performace. It may be beneficial for you for me to repeat some of our analysis here. For my discussion below, I will refer to the student as Joe.

1. On the problem of rolling down the incline. Joe got a torque which is mgRcos(theta). He said that it was just "a careless silly mistake". There is a comonsense technique which may be helpful in checking one's answer. This is to consider extreme situations, and see if the the expression makes sense. For instance, here if we set theta=0, which corresponds to a flat surface, we should expect a zero acceleration which contradicts the present answer torque=mgR.

2. Joe then proceeded to explain that since he made a silly mistake, he figured out a=(5/4)gcos(theta) as the correct answer. He said that his improved answer should be a=(5/4)gsin(theta). This answer is still no good. To see this let us set theta=90 deg. The improved answer leads to a=5g/4. The acceleration should never exceed g!

3. We then turned our attention to the problem of two-satellites. Here the question concerns the effect due to the doubling of the radius. Since gravity has an inverse-square law, associated with the doubling of the radius, one should get a factor of 4. Joe gets a factor of two. He says that he understands what goes on. Unfortunately the very "silly mistake" takes us from the inverse second-power law to the inverse first-power law. The description implied by these two power laws is completely different.

I would like to impress all of you, that physics is different from mathematics, in that physics is the disicpline which describes and predicts what takes place in nature. In order for us even a chance to understand nature, we need to use precise logical thinking. For example, the difference between "sine" and "cosine", "factor of two" etc must be taken seriously. They are not merely symbols on the paper, they do lead to different predictions in nature.

In order for the students to do well in this class, they are required to do rigorous manipulation of symbols. Remember they represent what goes on in nature. Train your self to be rigorous in algebraic manipulations.

Typically a Test question involves 2-3 steps logical reasoning and manipulations. When one does not take each step too seriously, one cannot perform well. One gets very few questions right. As one approaches each question in a more systematic and serious way, he/she will begin to perform.

To those who did poorly in Test 3, I invite you to do a self-evaluation on Test 3 (the concept on self-evaluation is explained in "Improve your study habits through self-evaluation") to see what it takes for YOU to get 100% correct. As you prepare for Test 4, you should ask yourself what it takes to understand the material "completely" not just to understand it "roughly".