light inverse square law
the intensity of light is inversely proportional to the square of the distance from the light source. As the distance between the light source and the plant increases, the light intensity decreases.
sound inverse square law
We can now think of this decrease in sound intensity in terms of decibels: So what does this mean in real life? Basically, if we are in a situation where the inverse square law is obeyed, as we double the distance from a sound source, the sound intensity decreases by 6 dB. This is referred to as the inverse square law.
gravity inverse square law
Gravitation is the attraction between objects that have mass. Newton's law states: The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance.
electrostatics coulomb's law
The law states that the magnitude, or absolute value, of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the squared distance between them.
The mole and Avogadro's number
One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions). The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant.
602,000,000,000,000,000,000,000 atoms one mole
E=mc2
energy equals mass times the speed of light squared
Einstein's most famous equation describes the relationship between energy, mass, and the speed of light. It says energy (E) equals mass (m) times the speed of light (c) squared (2), or E=mc2.
energy equals mass times the speed of light squared
square and square roots
Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.
vector math
a fixed vector with the following coordinates ie. components,
a[3 1 2]
in other words,
ax = 3,
ay = 1,
az = 2,
The magnitude (length) of the vector is,
length = sqrt((ax * ax) + (ay * ay) + (az * az))
length = sqrt(9 + 1 + 4) = 3.742
Given vector a its xyz components are calculated as follows,
x = ax/length
y = ay/length
z = az/length
As a "worked example" the vector shown in figure 1 has the xyz components of 3, 1, 2 and a length of 3.742. Therefore, a normalized copy of the vector will have components,
x = 3.0 / 3.742 = 0.802
y = 1.0 / 3.742 = 0.267
z = 2.0 / 3.742 = 0.534
