Becoming an expert in anything involves practice - lots of it. Pianists play the same scales over and over until they become second nature. A gymnast will practice somersaults until her body can perform the motion effortlessly. Physics is no different. In order to be able to solve physics problems, you will need to practice many hours and build up your mental muscles.

Consider the example of the gymnast. During a floor routine, a gymnast might undergo the following sequence. She runs, jumps, lands, jumps again and flips, then lands, does a roll, and ends the routine with a curtsy. Before she even begins to learn this routine, she must become an expert at each of the individual parts separately, then she can combine them into one fluid motion. It's no different with physics problems. You'll start by learning small operations and procedures. Eventually you'll be able to do the small parts with ease, and can then combine them into larger solutions to more complicated problems. She can even combine them into new routines that perhaps were never done before.

Continuing the analogy of the gymnast, it's probably also obvious that the only way for her to learn any of the parts of her routine, is by doing them over and over. At first, she'll fall when trying to do the flip. It'll hurt and she'll be embarrassed. But, eventually, she'll get it. No matter how many times she watches a teammate or coach do the same thing, she still needs to *do it herself*. The same process is true for physics problems. You have to *do problems yourself*, over and over until they become routine. It's easy to watch a professor or TA or friend do the problem, then say in your head, "oh yeah, I could do that when I need to, like on a test." The cold truth is, you won't be able to. Not without practice.

400 years ago, Galileo wrote that the book of nature is written in the language of mathematics. While much of science has changed since then, this basic statement still holds true. To understand the natural world at almost any level, mathematical analysis is required. This means you have to be able to work with geometrical objects, handle algebra, and maybe do some calculus.

The math you must be able to do, effortlessly:

- Trigonometry
- Algebra
- Functions
- Calculus (for 207/208 only)

Hopefully, your math classes have gotten you up to speed with these topics. If not, then it paramount that you take time to learn them. Physics will be *hopelessly hard* if you struggle with the notion of the inverse tangent or get stuck while manipulating fractions. It would be like taking a class on Italian cinema, in Swedish, without knowing a word of either language.

One of the most common things I hear from my side of the desk, is "I understand the concepts, but have trouble doing problems." If you find yourself saying this, the chances are good that you actually don't understand the concepts either. The concepts are the scaffolding that supports us while we do the problems. So, if your conceptual understanding is solid, then working through problems, while hard, is not impossible.

Introductory physics is sometimes taught as a *find the equation, then plug stuff in* exercise. This is not the point of physics. I repeat, this is **not** the point. That would be like if English class was just all about filling in the blanks in sentences or memorizing definitions of words.

After working with students on problems for several years, I've noticed a few things that often make solving problems harder. You might think these are good ideas, but they are not.

Do not plug your values in at the very beginning of a problem. This cannot be stressed enough. Give the quantities of interest in your problem variable names to start. Leave the equations in terms of the variables until the very last step. In fact, forget about the actually quantities completely while doing the problems. They will weigh you down like concrete blocks on your feet.

If you do not know the value for a given variable, do not set it equal to 1, or just remove it from the equation. This will not make things better. It could be the case that this particular variable will end up canceling out later on.

Do not do the problems on your calculator. Do them on a piece of paper, then use the calculator to solve the final result, if a numerical answer is needed. Sometimes, we don't care about a numerical answer and just want a relationship as the final result.

Draw pictures. The physical universe occupies space. As we seek to understand that universe, creating simple representations of phenomena in graphical form can help immensely. They don't need to be ornate drawing of reality, just simple sketches with lines and dots and vectors and labels.

Use a lot of paper. It breaks my heart to see people trying to do problems in the margins or on the back of a receipt. Get a notebook with lots of blank sheets. Or a ream of loose leaf sheets and a folder. If you need scrap paper, come see me and maybe we can find some around campus. (Sorry, trees. The only way we'll be able to protect you in the future, is by using some of you now to learn about nature.)

Do problems more than once. At the gym, do you do 1 pushup, then move on? No, you do 20 pushups. Repetition strengthens muscles. The same is true for physics muscles.

After you do a problem, try tweaking it a little and solving the new problem you've created. A simple example:

- Original problem: A car is traveling at 20 meters per second for ten seconds. How far has it traveled? Answer: 10s × 20 m/s = 200 meters.
- New, altered problem: A car is traveling at 20 meters per second. How long will it take to travel 200 meters? Answer: 200 m ÷ 20 m/s = 10 s. Yay!

Work with colleagues, but also make sure you can do the problems all by yourself.

Improving your conceptual understanding of physics principles can be a challenge. In my experience, the absolute best way to improve it is by having to explain it someone else. This an activity you'll have to be proactive about. Grab a friend, your little brother, a stranger on the subway, and say: "let me explain momentum to you." And, just quoting an equation isn't explaining something either. Pretend the person is 6 years old and doesn't know what p = mv implies. Write a story or describe a scenario that illustrates the concept in question. Having to *create* something demands understanding.

In closing, physics is hard. Anyone that says otherwise is probably lying or insane. You're going to make mistakes. That's normal. What you do after the mistake is made will determine your success in this course. (*Hint: analyze your error and explain to yourself why what you did is wrong.*) Lastly, don't wait until the day before the test to come see me. I have office hours and am usually available for appointments.