4 ms·
Another good example of this is the relationship between the period of a pendulum (T), its length (L), and the acceleration due to gravity (g). Since L is measu
by d_burfoot 4y ago
Another good example of this is the relationship between the period of a pendulum (T), its length (L), and the acceleration due to gravity (g). Since L is measured in m(eters), T is in s(econds), and g is m/s^2, there is only one way to combine these quantities that will give the right units : T ~ sqrt(L/g). And that's the right answer, up to a constant.
- kkylin 4y agoAnother nice example from mechanics is Kepler’s third law.
- danuker 4y agoThermal conductivity (W/(m⋅K)) is a counterexample. The meter is a trap. You can't just multiply the thickness of the material (scalar meters) to get Watts vs. temperature difference. You need to DIVIDE by it to get conductance (W/(m^2⋅K)) and THEN figure out the area the transfer is occurring over.
- pvillano 4y agoA similar unit exists for electrical resistivity. ρ := Ωm²/m. To calculate the resistance of a specific piece of wire, plug in the intrinsic property of copper (resistivity), and the dimensions of the specific wire. Out comes resistance. Ω(wire) = ρ(copper) × length ÷ area Where things get weird are thin films, ICs, and pcb traces with constant thicknes. The unit of sheet resistance is ohms per square. Because resistance increases with length and decreases with width, multiplying both by the same number doesn't change the resistance. Any square cut from the same sheet of copper has the same resistance between two opposite edges.