## 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: 1/10
^{7} of arc of a meridian from equator to pole
- Present definition: distance travelled by light in a certain number of seconds

- area: m
^{2}
- volume: m
^{3}

### 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 / distance
^{2}
- "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 / s
^{2}
- Unit of pressure: pascal [Pa] = N / m
^{2}
- Unit of work, of energy: joule [J] = N m
- Unit of power, of energy flow per unit time: watt [W] = J / s

2020-05-14

MASUDA Kooiti