Exam 1

(This is a reproduction of the email message sent to everyone on October, 16.  Note the exam date = October 23, Friday)
This email message is to give you a short guide on how to prepare for exam 1. 
Please make sure that you know how to do (1) examples/quizzes that I discussed in class (they may or may not be in my lecture notes on the web! -- please check your notebook), and (2) homework problems.  
If you can do them alone [i.e. all by yourself] without memorizing any equations other than the cribsheet equations (see "Course Materials" in WebCT), you are in excellent shape for the exam.  The exam will cover materials in my lecture notes 1-6, chapters 1-3 of the textbook, and homework sets #1 and #2.  Important topic titles are "1D kinematics (free fall), vectors, circular motion, relative velocity, projectile motion."  
My exam will consist of 3 problems.  Each problem will be very very similar, if not identical, to either one of my examples in class or one of my homework problems, excluding extra credit problems.  For each problem, you will need to show your complete work how you go from the basic equations in the cribsheet to your solution.  You would need to clearly define the coordinate system (the orientation and the origin), and to show coherence in your solution so that a knowledgeable person (TA) can clearly see your understanding of the physics.  Use my homework solutions as a study guide, but not as something that you want to memorize to "reproduce exactly."  You may have to "fill in the gap" for some of my homework solutions, if or since they are "a bit too brief."  If you just scribble something here and there, without really being coherent, then you may get close to 0 points.  
Any equation other than those given in the cribsheet will have to be derived from the cribsheet equations.  For instance, h = v02/(2g) for a ball tossed into air will have to be derived.  (The equation v2 - v02 = 2a (x-x0) can be used to derive it.)  Also, the equation such as d = v02 sin(2 heta)/g will have to be fully derived.  There will be no problem solely dedicated to the sig-fig, but showing your understanding of the sig-fig will be part of some problems, and you may be deducted some points if you mis-treat sig-figs.  
You can, and should, bring your calculator, memory cleared. 
Lastly, note that the deadline for homework #2 is extended to 10/20/09 07:00 pm (note the different time).

How to do physics problems?

1. Set up a coordinate system (CS) for space. The origin of the coordinate system and the positive direction of each axis should be chosen to make the problem the least complicated mathematically. One general rule is that you set up the coordinate system so that the motion of interest occurs at positive values of the position coordinates. The origin of the CS and the origin of the time should be chosen very clearly and as conveniently for the problem solving as possible. This is quite essential.
2. Recognize important events at specific values of space and time, and assign symbols for the space time coordinates and the velocity values for those events. Usually there are two or three important events in a problem. For instance, for a tossing-a-ball problem, "a ball leaving the hand" and "the ball reaching the top" may be two important events. These events can be named i (initial), f (final), or H (hand), T (top). Use symbols for time, space, velocity for each of these important events. For instance, t_H, x_H, v_H, and t_T, x_T, v_T, can be used to specify time, space, and velocity for these two events.
3. Recognize symbols whose values are known and those whose values are not known. By the choice of origins in space and time (step 1), some symbols defined in step 2 will turn out to be zero. Some other value will be zero because of physics (v_T=0 since the velocity is changing direction just at that point).
4. Examine the "fundamental equations" to use. For the example above, x = x₀ + v₀ t + 0.5 a t² and v = v₀ + a t, are those equations to use. Taking the time origin at the event H, notice that t_H=0, v_H=v₀ in the above example. Also, assuming that the x axis was taken to be pointing up, the acceleration a will be a negative value a = -g.
5. Set up "specific equations" to solve, by plugging in time, space, velocity values for the important events into the "fundamental equations." The specific equations to solve should not contain general variable symbols such as x and t. Instead, they should contain specific symbols that you defined in step 2 (e.g., t_H, x_H, v_H, and t_T, x_T, v_T). Solve these specific equations for unknown symbols.
6. Do not plug in the actual values of known symbols, until the very last step. Carry out calculations with symbols instead.
7. Interpret the final result in relation to the original question.
8. (addendum to 7) Always be clear about the meanings of symbols, per each problem. Physics problems are rarely those kinds where you can simply plug in a few known values into the textbook equations to get the answer. The same symbol can be, and are, used to mean different things in different problems. Always know which direction the position axis is pointing to, where the spatial origin is, and where the time origin is. Know how to relate the numerical answer that you get from solving your specific equations (steps 5-7) to the required answer of the original question.