A few facts to memorize for "back of the envelope" calculations:
1 inch
» 2.5 cm (actually 1 inch = 2.54 cm)1 foot
» 30 cm (actually 1 foot = 30.48 cm = 1.09 yd.)1 meter
» 3 feet = 1 yard (actually 1 meter = 3.281 feet)8 km
» 5 miles or 1 mile » 1.5 km (actually 1 km = 0.6214 miles and 1 mile = 1.609 km)
1 meter per second
» 2 miles per hour (actually 1 m/s = 2.237 mile/h)25 m/s
» 55 mile/hour1 Newton
» one stick of butter = 1/4 lb. (actually 1 Newton = 0.2248 lbs)1000 Newtons
» Dan Ackroyd ( actually 1000 N = 224.8 lbs)1 Joule
» 3/4 ft-lb (actually 1 J = 0.7376 ft-lb)1000 Joules
» the work done in lifting 100 pounds over your head
1 liter
» 1 quart (actually 1 liter = 1.06 quarts)1 liter of water has mass about 1 kilogram. (depends on temperature, pressure, purity of water; many materials have a density quite close to water so this works fairly well for many materials. "A pint is a pound the world around.")
1 radian
» 60 degrees (actually 1 rad = 57.3 deg angle measure)p
radians = 180 degrees (halfway around the circle)0
° C = 32° F100
° C = 212° F
sin(0) = 0, sin(
p /6) = 1/2, sin(p /2) = 1, sin(p )=0, sin(-p /2) = -1cos(0) = 1, cos(
p /3) = 1/2, cos(p /2) = 0, cos(p )= -1tan(0) = 0, tan(
p /4) =1, tan(p /2) = "infinity", tan(-p /4) = -1SOH-CAH-TOA
Constants: Approximate values
p »
3 or 3.14g
» 10 or 9.8 m/s^2 (acceleration due to gravity)c
» 3 x 10^8 m/s (speed of light in vacuum)radius of earth
» 6000 km
Eventually you will memorize these unit definitions:
1 Newton = 1 kg-m/s^2
1 liter = 1000 cm^3
1 Joule = 1 Newton-meter
1 Watt = 1 Joule/sec
Some powerfully energizing facts (not worth memorizing)
1000 Joules
» the work done in lifting 100 pounds over your head » 1 Btu = energy needed to heat a cup of water one degree Fahrenheit.1 million Joules
» 250 Calories (kilocalories) » one glazed donut1 horsepower = 550 ft-lb/s
» 3/4 kW » power used by a toaster(actually 1 hp = .7457 kW = 745.7 W = 745.7 J/s)
For more information and some fascinating problems on approximation, see http://www.vendian.org/envelope/ .