Unformatted text preview: Quantities characterizing motion in two and three dimensions have
both magnitude and direction and are desaibed by vectors. Posi—
tion, velocity, and acceleration are all vector quantities, related as they are in one dimension: These vector quantities need not have
the same direction. In particular, ac—
celeration that’s perpendicular to ve
locity changes the direction but not
the magnitude of the velocity. Accel
eration that’s coljnear changes only
the magnitude of the velocity. In gen
eral, both change. Vectors can be characterized by magnitude
and direction or by components. In two
dimensions these representations are related
by A
A: VA3+A; and (belief I AX = A6056 and A), = AsinG Components of motion in two perpendicular directions are inde
pendent. This reduces problems in two and three dimensions to
sets of onedimensional problems that can be solved vvith the
methods of Chapter 2. A compact way to express vectors involves
unit vectors that have magnitude 1, no
units, and point along the coordinate axes: When acceleration is constant, motion is described by vector equations that generalize the one~dimensional equations of Chapter 2: i7=ﬁu+at 1?: An important case of constant—acceleration
motion in two dimensions is projectile
motion under the inﬂuence of gravity. 5’
= 1: tan 6 — ‘x2
y 0 21102003260 FD + E": + 5:2 Velocity is the rate of change of the position
vector 3‘: g
dr
Acceleration is the rate of change of velocity:
92
dr _.
V 5: In uniform circular motion the magnitudes of
velocity and acceleration remain constant, but
their directions continually change. For an ob«
ject moving in a circular path of radius r, the
magnitudes of ii and 17 are related by a: vzlr. 17 ...
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 Spring '07
 KOPP
 Physics

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