Learning goal: to introduce the idea of physical dimensions and to learn how to find them. physical quantities are generally not purely numerical: they have a particular dimension or combination of dimensions associated with them. thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. although feet and inches are different units they have the same dimension--length. find the dimensions [v] of volume. find the dimensions [v] of speed. express your answer as powers of length ( l), mass ( m), and time ( t)

volume : {l}^3

speed: (l)^1*(t)^-1

Explanation:

Volume is a measure of 3 dimensional space. It is expressed with 3 orthogonal lengths. The volume of a box would be the product of it's height, width and length. These 3 are longitudes that can be expressed in meters, feet, inches, etc. Because these are 3 longitudes multiplied the result will be a cubic longitude (l)^3.

A more general method for finding a volume is to use integral calculus:

This is for Cartesian coordinates. Cylindrical and spherical coordinates can also be used.

Speed is defined as the rate of change in position respect of time:

For movement in one dimension.

For movement in 3 dimensions you calculate the speed component of each space direction and express them as components of a speed vector:

This is a vector of velocity components, each one is expressed as a division of a longitude over a time, so speed components have dimensions of (l)^1*(t)^-1

The speed vector has a magnitude that is obtained with the Pitagoras theorem:

Since each component is squared, added together and then the square root is taken this magnitude is also in (l)^1*(t)^-1

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​