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PH1110A2008
Assignment 1
Due at 11:59pm on Friday, August 29, 2008
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Vector ComponentsReview
Learning Goal:
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
,
and
, along the
x
and
y
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
.
Part A
The figure shows the standard way of measuring the angle.
is measured
to
the vector
from
the
x
axis, and counterclockwise is positive.
Express
and
in terms of the length of the vector
and the angle
, with the
components separated by a comma.
ANSWER:
,
=
In principle, you can determine the components of
any
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
and
will have the appropriate signs and values.
Unfortunately this way of representing
, though mathematically correct, leads to equations that must be simplified using trig identities such as
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This note was uploaded on 10/13/2008 for the course PH 1110 taught by Professor Kiel during the Spring '08 term at WPI.
 Spring '08
 Kiel
 Physics

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