Advent
drorzel | December 3, 2011We kicked off the countdown to Newton's birthday with his second law of motion, which is almost but not quite everything you need to understand and predict the motion of objects. The missing piece is today's equation:
This is the full and correct definition of momentum, good for any speed all the way up to the speed of light. Newton's second law tells us how the momentum changes in response to a force, but in order to use that to predict the future, you need to know what momentum is, and that's where this equation comes in.
(Wouldn't it make more sense to do this first, and the second law…
drorzel | December 2, 2011We kicked off our countdown to Newton's birthday with his second law of motion, so the obvious next step is to go to his third law of motion:
This one was also originally in Latin, because that's how Ike liked to roll:
Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.
In English, this comes out as:
Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
That first…
drorzel | December 1, 2011It's that time of year again, when we count down the days to Isaac Newton's birthday (according to the Julian calendar, anyway), and how better to mark this than with mathematics? Thus, I'll post an equation a day until either Christmas Eve or I run out of ideas, and talk about what it means and why it's important for physics.
Since this is, after all, a celebration of Sir Isaac, let's kick things off with arguably his most famous equation:
OK, it might not look familiar in this form, but this is, in fact, the full and correct statement of Newton's Second Law (written in modern notation),…