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Motion on a Curved Racetrack
Theory
: The text proves that the radial (centripetal)acceleration component points to the center of the
circle and has a magnitude of
a
r
=
v
2
r
when an object moves at speed v in a circle of radius r.
This is true whether or not the object is changing speed. If the object changes speed it will also
have a tangential component of acceleration.
Example
.
You drive a gocart around a go cart track, consisting of two arcs (radii shown on diagram) connected by
two straight segments as shown. Indicate an acceleration of zero by writing
a
= 0.
(a) You drive at a constant 5.0 m/s. What is your
acceleration (at points W, X, Y, and Z? Magnitude
should be a number. To show direction, draw the
acceleration vector (==>) at each point. Be sure that
your vectors are to scale relative to each other.
(b) Your friend is more adventuresome. She drives the small arc at 5.0 m/s, then accelerates on the lower
straight segment from 5 m/s to 15 m/s, which takes 5.0 s, drives the large arc at 15 m/s, and then
slows back to 5.0 m/s in 5.0 s on the top straight segment. Find your friend’s acceleration for the
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 Fall '09
 LIND
 Acceleration, Velocity

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