Equation of the Day: F = ma

Now for something non-curmudgeonly - the equation of the day. Let's kick this off with a classic, Newton's Second Law of Motion, or F = ma.

In words, it says "Force equals mass times acceleration." Force and acceleration are vectors. They have both a magnitude and direction. This makes sense. If I apply a force in some direction, I expect to see the object I am applying the force to accelerate in that direction.

Mass is a measure of the resistance of a body to an applied force. That seems like a circular definition, since it really just says mass is equal to force divided by acceleration, which is exactly what Newton's Second Law of Motion says. But mass shows up in other places too, like Newton's Law of Universal Gravitation. In fact, it seems kind of bizarre that the same property shows up in two disparate equations like that and did not appear as two different constants. And it shows up in another famous equation too: E = mc^2. Hmm, maybe all these things are related.

Newton's three laws of motion form the basis for classical mechanics. They can explain how most everyday things work and are used for everything from design of automobiles, aircraft, boats and bridges to predicting the weather. The field of statics is based on the second law with the acceleration equal to zero. The field of dynamics is applying the second law to accelerating systems. You can put a lot of study into one simple equation, and you can learn a lot about the world from it.