## Simplifying Mathematics: Introducing Vectors and Vector Addition

[caption id="attachment_23153" align="alignright" width="480"] Magnetic vector force field[/caption] We all know how to add, subtract, multiply and divide ordinary numbers, even if basic units are attached to them such as gallons, apples, feet, tons, and so forth. 4+3 = 7 5 lbs x 3.2 = 16 lbs These two examples illustrate pure numbers in the first instance, and simple quantities in the second instance. Introducing Vectors: What About Direction? What if we toss in direction? Imagine a huge square, 5 miles on a side. We have to travel along the perimeter to travel from Point A to Point B, and then on to our destination, Point C (see the image). We thus travel 10 miles to reach Point C. If we could travel "as the crow flies", we would only…

## Converting Gas Temperature to Particle Velocity

[caption id="attachment_18761" align="alignright" width="440"] Atoms or Molecules of Gas[/caption] Unlike liquids or solids, whose atoms or molecules have greater correlation with each other, gas atoms and molecules move somewhat independently of each other. This is to be expected. A gas occupies a much greater volume than a corresponding liquid. This independent behavior allows us to calculate the root-mean-square velocity of gas particles directly from temperature. Tweaking the Ideal Gas Law We derive this equation from another well-known equation, the Ideal Gas Law equation. Algebraically, that equation is written: PV = nRT where P is pressure, V is volume (not velocity), n is the number of moles of gas, R is the ideal gas constant and T is the temperature. By combining the above equation with derivatives of Boltzmann's equation, we…

## Distance, Velocity, and Acceleration

[caption id="attachment_3512" align="alignright" width="440"] Porsche 911 image - CCA 2 Generic[/caption] Do you know the relationships between distance, velocity, and acceleration? In learning about a matter, the primary obstacle is likely to be understanding the concept of it. For instance, as a young teen, I was introduced to algebra. Algebra is the first form of mathematics that contains not only numbers, but letters as well. Numbers are constant (after all, 3 is three), but letters are used to indicate variance in value, i.e. they are variables. Distance The concept of distance is so very simple, it is taken for granted. But should it be? Some young ones may not fully comprehend the concept of distance. That being said, we will assume here that the reader and his or her pupil…