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