Fall 2010 UBC

What is on the exam?

I’m getting a lot of “is this on the exam?” and “will you give us this formula”?  I’m specifying some answers to these things here:

0) Formulas.  I’ll put the following curvature formula on the exam if you will need to use it, because it is, in my estimation, too time-consuming or just plain annoying to re-derive yourself:

\kappa = \frac{| \mathbf{r}'(t) \times \mathbf{r}''(t)|}{|\mathbf{r}'(t)|^3}

The other curvature formulas are respectively a) the definition (change in unit tangent with respect to arclength) and b) derived in one step using chain rule (see equation 9 in Chapter 14.3).

1) Yes, I could ask you to compute the centre of mass or moment of inertia, but I would remind you of the formulas if I do this.  Don’t pointlessly memorize the formulas, but it can be instructive to ponder why they are what they are.

2) Yes, I could ask you about tangential and normal components of acceleration, and paths of projectiles.  You should know the formulas, but these formulas can be re-derived if necessary, so the best is to study that derivation, as it is excellent review of the concepts of Chapter 14.  In doing so, you’ll probably memorise the formulas by accident, as they’re very simple.

3) Yes, I could ask you about Kepler’s laws of motion, but we didn’t do much more with them than learn their statements.  So just understand the statements.

4) Yes, The Law of Gravitation is a fine example for vector fields.  Be familiar with the example.  You should probably know the form of the field (how does it depend on \mathbf{r} or r), but don’t memorise the constants!

I will add to this list if there are specific topics you’re wondering about.  But the general answer is “yes, if it’s part of the course, it could be on the exam!”

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