Mathematica Understanding Impulse, Intensity & Inertia

[SeManTics]

Could someone explain to me the mathematical differences between impulse, intensity, and inertia? I mean, they all start with I's, but I still cannot determine any mathematical precision instead variation among these three.

 

[Chronos]

You are basically trying to distinguish the difference between scalar and vector quantities. Do a web search. Scalar forces merely have magnitude, vector forces have magnitude and direction.

 

[HallsofIvy]

First, there are no "mathematical" definitions of these because they are not mathematical concepts. I think you want the definitions of the words as they are used in physics (though the same words are used in other fields with different meanings).

"Impulse" is specifically defined as "change in momentum" and can be written as force times time: applying a specific force to an object for a specific length of time will accelerate the object, changing its velocity and, thus, its momentum. If you apply force F for time T, since acceleration is F/m (speed per unit time), the speed of the object will have increased from v₀ to v₀+ FT/m. The momentum will have changed from mv₀ to mv₀+ FT, a change of FT.

"Intensity", I believe, does not have a meaning in any specific field of physics but simply refers to a "how strong" something (light, sound, force, etc.) is, typically given as a single number. If the quantity in question is given as a vector, its intensity is typically the length of the vector.

Finally, "inertia" measures an objects resistance to change in its motion. That is typically what is meant by "mass"- although the question as to why that "mass" is the same as "mass" used to calculate gravitational force (in other words, why all objects have the same acceleration under gravity) is a very deep one.

 

[Tide]

Intensity refers to power (energy per unit time) flow through a surface. For example, light intensity would be measured in Watts per square centimeter.