Circular motion and Inequalities

On Friday in Mr. Ambrose’s physics class, the students did an experiment. They ran a string through a tube and connected one end to a weight; the other end was connected to a small rubber stopper. One person spun the stopper in a circle, and the other one timed it. The idea was to measure the period and the radius, calculate the speed and centripetal acceleration, and compare it with the force provided by the weight. Most of them had pretty good experimental data and relatively low errors, once they did the calculations properly. In the rush of doing the lab, there were quite a few careless errors, but they’re smart enough to see that if the results are THAT far off, something is wrong. I helped several of them find their mistakes, and many times it was a decimal point in the wrong place, or reading a number out of the wrong column. Running a “sanity check” on results is a good skill to get in any field, so I think making those errors actually had a use. Today, they moved on to doing problems on curves – things like how fast can a car go around a curve without skidding. They haven’t gotten through banked curves yet, but that will be the next topic, and then they’ll move on to universal gravitation.

In Ms. Colwell’s class, they’ve been working with inequalities, and graphing them on number lines. I’ve mentioned that inequalities are useful in linear programming, and it turns out they’re actually going to cover that. Since that falls into the area of optimization, Ms. Colwell is going to give me a class period next Friday to talk about optimization and non-linear programming. Obviously, I can’t teach them in one class what it takes multiple graduate classes to learn, but I can give them an idea of what you can do with this type of math and why it’s important.