Physics
The math physicists use every day
27 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
QuadraticsThrowing a ball: the quadratic arc
Every throw, jump, and fountain draws a parabola.
Linear EquationsSpeed, distance, time: how long is the drive?
Distance is speed times time. Rearrange it and you know when you’ll arrive.
Linear EquationsE6B density altitude: the 120-feet-per-degree rule
Pressure altitude, plus 120 ft for every degree warmer than standard. Quick enough to do in your head.
Linear EquationsHooke’s law: how far does the car sag when you load it?
A spring squeezes in a straight line with the load: twice the weight, twice the sag, until it hits the stops.
Ratios & ProportionsTorque: how hard to pull the wrench, and what an adapter changes
Torque is force times distance. A longer handle takes less push, and an adapter that adds length means you must set the wrench lower.
Exponents & LogarithmsBrightness vs. distance: the inverse-square law
Move a light twice as far and it gives a quarter of the light. Photographers call that two stops.
QuadraticsJumping on the Moon: the same leap on other worlds
Same legs, same launch. Weaker gravity stretches the parabola, and the motion plays in real time.
Arithmetic & Number SenseE6B weight and balance: where the center of gravity lands
The CG is a weighted average. Load people, bags, and fuel, and watch the dot move in the envelope.
Linear EquationsHome heat loss: where does the heat go?
Heat leaks through each surface in proportion to area and temperature difference, divided by R. Windows and drafts punch far above their size.
Linear EquationsStress and strain: how much does a rod stretch under a load?
Stress is force per area. Divide by the material’s stiffness and you get the stretch, until it yields and stays bent.
VectorsCrossing a river: where you aim vs. where you end up
Your speed and the current add as arrows. Aim straight across and you drift; aim upstream and you can land right on target.
VectorsHanging a hammock: why the 30° rule works
Your weight and the two strap pulls are arrows that must add to zero. Hang it tight and flat, and each strap pulls with several times your weight.
VectorsCrosswind landing: splitting the wind into two parts
Pilots break the wind into “along the runway” and “across it.” That’s vector math at 60 knots.
Exponents & LogarithmsDecibels: why two speakers aren’t twice as loud
Sound is measured on a log scale. Double the speakers: +3 dB. Double the distance: −6 dB.
Exponents & LogarithmsThe rocket equation: why rockets are almost all fuel
Speed grows with the logarithm of the fuel. Double the tank and you get far less than double the speed.
QuadraticsWing lift: why twice the speed means four times the lift
Lift grows with airspeed squared. Bernoulli, angle of attack, thin air, and the stall, all on one curve.
Exponents & LogarithmsOrbits: how fast to go around and never come down
An orbit is falling and missing the ground. Square roots and a 3/2 power set the speed and the period.
Exponents & LogarithmsE6B density altitude, exact: standard atmosphere and humidity
The full standard-atmosphere formula, plus the dew point. Humid air is lighter, so it flies higher.
Exponents & LogarithmsE6B true airspeed: why you’re faster than the dial says
The airspeed indicator feels air pressure, not speed. Thin air at altitude makes true airspeed higher.
Exponents & LogarithmsRapid cooling: 135 °F to 70 °F in two hours
Cooling slows as food nears the fridge temperature. A logarithm says how long it takes, and why shallow pans win.
TrigonometryCrank and piston: turning rotation into back-and-forth
A crank turns a circle into a straight-line stroke. The connecting rod bends the motion away from a pure sine wave.
VectorsSolar panel tilt: how much sunlight it catches
Point one arrow at the sun and one straight out of the panel. Their dot product is the share of full sunlight the panel gets.
Differential Equations & TransformsDoor closer: slam, bounce, or glide
One damping knob turns a slam into a glide. Where two dots (the poles) sit tells you which.
Differential Equations & TransformsWhy the shower goes hot, then cold
You react to water that left the tap seconds ago. Delay plus impatience makes the swing, and one number predicts it.
Exponents & LogarithmsThe Bartz equation: how regenerative cooling keeps a rocket throat from melting
Heating grows with chamber pressure to the 0.8 power and peaks at the throat. The fuel flows through the wall to carry it away.
Calculus (intro)Speed from a position graph: the derivative
The steepness of a position graph is the speed. Shrink a secant line down to a tangent, and you have the derivative.
Calculus (intro)Distance from a speed graph: area under the curve
Speed times time is distance, one thin rectangle at a time. Add more rectangles and the total closes in on the exact area: the integral.