Q2: Show that (A, Ay, A) are related to (Ap, A,Az) using the following matrix: cos o -sin o 0 Ao A Ap A, A, A2 sin o cos o %3D 1 Note that, in cylindrical coordinates, the unit vectors are related as follows: a, = cos o a sin o as a, = cos o a, + sin o a, = sin o a, + cos o as a =-sin o a, + cos o a, ay a a. %3D a, = a, %3D

Principles of Physics: A Calculus-Based Text
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ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
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Chapter10: Rotational Motion
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Q2: Show that (Ax, Ay, Az) are related to (Ap, Ag, A,) using the following
matrix:
cos o -sin o 0
Ap
0.
cos o
sin o
Ay
A,
0.
1
A,
Note that, in cylindrical coordinates, the unit vectors are related as follows:
a, = cos 6 a,
sin o as
a, = cos o a, + sin o a,
a, = sin o a, + cos o a
a, = -sin o a, + cos o a,
a, = a,
a, = a.
Transcribed Image Text:Q2: Show that (Ax, Ay, Az) are related to (Ap, Ag, A,) using the following matrix: cos o -sin o 0 Ap 0. cos o sin o Ay A, 0. 1 A, Note that, in cylindrical coordinates, the unit vectors are related as follows: a, = cos 6 a, sin o as a, = cos o a, + sin o a, a, = sin o a, + cos o a a, = -sin o a, + cos o a, a, = a, a, = a.
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