07Mar 2016 by Vincent Summers No Comments

What are Radians? Where Do They Come From?

Mathematics
Consider a simple equilateral triangle (a triangle that has 3 equal sides and 3 equal angles). Most high-school students know the three angles of such a triangle are 60 degrees (60°) each, for a total of 180°. But degrees is not the only unit used to quantify an angle. Alternately radians can be used. What are radians? Are they just another number? Where do they come from? Degrees Before we get into radians, however, let’s consider where degrees came from, and why it may not be the best choice for the measurement of an angle. If you are facing north and turn to the east, you have turned 90 degrees. Now turn south and you’ve turned another 90 degrees. Turn west, another 90 degrees. Continue the turn so you once…
Read More
17May 2015 by Vincent Summers 1 Comment

Massless Strings and Frictionless Pulleys

Physics
Massless strings and frictionless pulleys? Whoever heard of such things? I attended Drexel University. Well, at first it was the Drexel Institute of Technology. I majored in chemistry. It was strongly suggested I major in chemical engineering. But I refused to change. Why? Because I didn't care what use humans put chemistry to. I loved chemistry and that was all there was to it. Unfortunately (or so it seemed at the time) majoring in chemistry didn't mean all my courses would be chemistry courses. Physics - Massless Strings & Frictionless Pulleys Well—unavoidably—I was required to take a certain amount of physics. And introductory physics requires the use of simple mathematics, including calculus. But physics equations can be difficult to derive. Simplification wherever possible was the mandate. This simplification required us…
Read More