Velocity is the first derivative of position.
Acceleration is the first derivative of position and the second derivative of position.
Jerk is the first derivative of acceleration…
Similarly, the shear force in a member is the derivative of it’s curve.
The moment force is the second derivative…
What’s the third derivative? I know it’s something important, it’s been awhile.
An antenna F feet high can transmit/receive approximately 1.2*(Square root of F) miles. (Example: 100-foot antenna works for 1.2*10 = 12 miles). Or, if you’re F feet tall, you can see 1.2 F miles standing on the beach (Cecil did a column on this – it’s a derivation using the Pythagorean equation).
One nautical mile equals exactly 1.852 kilometers. This is not an approximation like km to feet. It’s EXACT, like 5280 feet to one statute mile, or 12 inches to one foot. This may seem like a trivial distinction, but it’s important to software geeks and navigators.
Not a problem. It’s used in situations where the acceleration happens quickly enough that the motion does its thing before the materials start reacting.
I’ve never heard of a “jerkmeter”, I suspect that’s a bit of gratuitous editing. The only time I’ve measured it, we used accelerometers that were tapped into a blast wall and simply took the derivative of the curve.
I forget the specifics, but I’ve also used jerk when analyzing high velocity impact dynamics. Metals are very cool, in that they can withstand pressures high above their yield strengths when said pressures are initiated very fast (impulse) and for a very short time period. It’s almost as if the metal becomes an incompressible liquid for a short period of time, and, in fact, that’s how explosive welds are analyzed.
And the derivative of a real number is xn^x-1. So the derivative of x^4 is 4x^3
Not a formula but a help for math classes, especially geometry. If you have a graphing calculator, I’m assuming a TI-83 cuz that’s what I have but I bet other brands do this as well, then you can program formulas into it so that you hit a a few buttons, input your numbers and it applies the correct formula. Check your manual for instructions on how to program.
The volume of a sphere is 4/3 pi r^3*.
Its area is the derivative of that, or 4 pi r^2.
The circumference of a circle is the derivative of its area, pi r^2 goes to 2 pi r.
*Note that the rank (size of power) is the same as number of dimensions in each case.
There are 124 pints in a keg (15.5 gallons times 128 ounces per gallon divided by 16 ounces per pint).
An acre is how much land one man and two oxen can plow in one day.
The sun travels approximately one degree around the sun each day.
If we have a three variable system, we can solve for any variable by covering up the other two. For example
distance
rate = time
If we cover up distance, we get distance = rate * time
If we cover up time, we get
distance
time = rate
Appoligies to Ignaz for not seeing their posting of Pythagoras.
In this vein, the true “safe” speed for corners, as advised by the yellow cautionary signs that come before them, can be found by doubling said speed and subtracting 10%. So, using your example, the maximum “safe” speed of a cautionary 45mph curve would be 90-9, or 81 mph.
I’m mostly kidding.
Maybe not exactly useful, but interesting if you like Pythagorean triangles; here’s a formula that generates every right triangle with integer sides. Take any two numbers M and N such that M>N>0. If you want only right triangles with the sides reduced to the lowest terms, further specify that M-N is odd, and that M and N have no common factors. Your two numbers then generate the three sides of a right triangle A, B, and C through the following formula:
A=M²-N² B=2MN C=M²+N². For example, M=2 N=1 gives A=3 B=4 C=5
So, for instance, the base ten log of 6.4 is 0.8. Remembering that powers of ten add one to the base ten logs, the log of 640 is 2.8. The log of the number of days in a year must be about 2.55 (the Windows calculator confirms it’s 2.562…).
This sequence is three threads interleaved. One of them is 1, 2, 4, 8. Another is 1.25, 2.5, 5, and 10 would be next (starting the next cycle). The third is 16, 32, 64, and in the next cycle 128, familiar powers of two, though they need a decimal point shift, and the 128 becomes 125, as this isn’t perfect but good to a percent or so. These patterns make it easier to remember the sequence.
With base ten logs you can do all sorts of things. Remembering this sequence as the question rather than the answer means you have powers of ten too. And multiplying these by 2.3 gives you natural logs, which are even more versatile.
if you take someone’s hourly rate of pay and multiply it by 2000 you have a decent approximation of their annual wage. (this obviously works in the other direction as well)
I know that. I was giving the useful approximation for those who can’t work out five-ninths in their head. And “Minus forty” is the temperature for which you don’t need to give the scale (use either formula above and substitute F=C).
