Since I’m getting ready to take the GRE Physics subject test, I’m trying to review my introductory physics.
Yeah, not the most fun sounding prospect, I know.
Thankfully, I really do love physics and I tutor introductory physics at a reasonably large university, so this shouldn’t be that hard. At least until I start running into the chapters on electrostatics and circuits. I found out recently that I forgot a lot about those topics.
Anyway, in case anyone is interested, I’m using a textbook called Physics for Scientists and Engineers. I picked it up for free when the physics department was getting rid of some old books.
So… the first chapter:
It covers about the first week of a physics class, as far as I can determine. It goes over SI units (the metric system – which I love, and I will forever wonder why it hasn’t been adopted by the United States already, because the English system is confusing and really quite useless), dimensional analysis, significant figures, scalars and vectors. Vectors get talked about a lot, because apparently they confuse people. After three years studying physics at the collegiate level, vectors are pretty straight-forward to me, but given that I will be spending the first two weeks in the tutoring center explaining them repeatedly I know that a lot of people find them confusing.
The easiest way to remember what a vector is to remember this:
Vector from Despicable Me actually really did describe what a mathematical vector is! A vector is a quantity that has magnitude (for example, 30 meters or 9.8 m/s^2) and also has a direction (north or down). Quantities like velocity, acceleration, momentum and force are vectors.
A scalar quantity has magnitude but lacks direction. A mass of 25 kg is a scalar quantity. The length of my driveway is 100 meters is a scalar quantity.
Interestingly, and much to the confusion of many of the people I tutor, speed is a scalar quantity. “I drove my car 60 km/hr.” This tells you how fast I drove my car but lacks a description of what direction the car is going in. The moment I say, “I drove 60 km/hr north on I-75,” I have now described the velocity of my car, and therefore used a vector quantity. (The term velocity is sometimes used interchangeably with speed in everyday conversation, but technically, by definition, velocity must describe the direction of the object as well as its speed, thus making it a vector quantity.)
Adding and subtracting vectors is another tricky concept for people, but all that requires is a little trigonometry and a bit of drawing. (I should go get my Intuos tablet to draw out my examples, just like I usually draw all over the blackboard!) I’ll likely get to demonstrate that when I start answering the conceptual questions and the problems at the end of the chapter.
