Physical quantities and SI units
[2020-05-14] I included this page today in order to explain "latitude" and "longitude".
I notice that the text of this page is too brief.
I plan to revise it.
Dimensions of space
Dimension of space, dimension of physical quantities ... different concept.
We live in 3-dimensional space, or 4-dimensional space-time.
3-dimensional space: position of a point can be expressed in 3 real numbers.
- linear orthogonal coordinate (Cartesian [=DesCartes] coordinate): 3 lengths (x, y, z)
- spherical cordinates (r, theta, phi)
- latitude, longitude, height ... variant of spherical coordinates. Note different conventions
Explanation of latitude and longitude
The shape of the earth is approximated by a sphere
(Not very precise).
Latitude ("lat") of point P, in a cross section of the earth, which includes point P and both poles
Longitude ("lon") of point P, in a view of the earth from the north pole
Unit of spatial dimensions
- length: metre [m]
- Original concept: 1/107 of arc of a meridian from equator to pole
- Present definition: distance travelled by light in a certain number of seconds
- area: m2
- volume: m3
Unit of time
- SI unit: second [s]
- day = 24 * 60 * 60 s ["*" means multiplication here]
- year = approx. 365.25 days
Concepts of "weight" and "mass"
Primitive concept "weight", "heavy"
differentiated scientific concepts "gravity", "mass", "density"
Basic roles of mass in physical sciences
- Law of motion (Newton; formulated later): force = mass * acceleration
- Law of gravity (Newton): force = constant * mass * mass / distance2
- "Conservation of mass" (typically Lavoisier)
SI unit of mass and force
- Unit of mass: kilogram [kg] (= 1000 g)
- Original concept: mass of water of l litre (a 10 cm * 10 cm * 10 cm cube) at 4 deg. C
- Official definition was changed recently. (I will check references if you want.)
- Unit of force: newton [N] = kg m / s2
- Unit of pressure: pascal [Pa] = N / m2
- Unit of work, of energy: joule [J] = N m
- Unit of power, of energy flow per unit time: watt [W] = J / s