10/13/08 1:09 AM
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Chapter 01 - Units, Physical Quantities, And Vectors
Due at 11:59pm on Tuesday, September 9, 2008
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A number written in scientific notation has the form
is an integer.
Consider the expression
. Determine the values of
when the value of this expression is written in
Hint not displayed
, separated by commas.
To introduce you to vectors and the use of sine and cosine for a triangle when resolving components.
Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable
calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and
fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or
about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector
quantities, resolving vectors into components is
the most important skill
required in a mechanics course.
The figure shows the components of
, along the
axes of the coordinate system, respectively. The
components of a vector depend on the coordinate system's
orientation, the key being the angle between the vector and the
coordinate axes, often designated
The figure shows the standard way of measuring the angle.
axis, and counterclockwise is
in terms of the length of the vector
, with the components separated by a comma.
In principle, you can determine the components of
vector with these expressions. If
lies in one of the other
quadrants of the plane,
will be an angle larger than 90 degrees (or
in radians) and
the appropriate signs and values.