12 Mar 2015

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PHYS 17200 - Modern Mechanics - Lecture 1_Matter and Interactions

Modern Mechanics

● uses a few fundamental concepts and principles that apply to all kinds of matter

and their interactions

● uses approximations to create simple models able to predict and explain an

enormous range of physical phenomena

● unites mechanical and thermal physics by creating models of ordinary objects as

systems of interacting atoms

● uses powerful computers and computer graphics to simulate and display the

behavior of realistic physical systems

Vectors

● So, a vector is represented by the triple of its components r_vector= <x, y, z>

which in the case of a position vector are just the position’s three coordinates.

● A position vector’s length is one specific example of the magnitude of a vector

magnitude of r = r_mag= sqrt(x^2+y^2+z^2)

● Multiplying all of a vector’s components by the same scalar factor produces a

vector parallel to the original one but with magnitude larger or smaller by the

same factor

● If the scalar factor is negative, the new vector actually points in the direction

opposite the original.

● Specifically, multiplying any vector by the inverse of its magnitude produces a

dimensionless vector parallel to the original

i.e. r_vector/r_mag = r_unitvector