Classical Dynamics Of Particles And Systems
5th Edition
ISBN: 9788131518472
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning India
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Question
Chapter 1, Problem 1.26P
To determine
The expression for
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Given a space curve C with position vector
r =
3 cos 2t i + 3 sin 2t j + (8t – 4)k
Find a unit tangent vector Urto the curve.
a) (-3/5) sin3t i+(3/5) cos 2t j + (4/5)k
b) (3/5) sin3t i+ (3/5) cos 2t j +(4/5)k
c) (-3/5) sin3t i- (3/5) cos 2t j + (4/5)k
d) (-3/5) sin3t i+ (3/5) cos 2tj - (4/5)k
518۹ من ٥۱۹۰
Example 2; find O between A¯and B?
A*=2î +3ƒ +k , B =3î -2j +k
Example 3; if 0=30o between A¯and B'find q
value?
A¯=2î +2j +4k , B'=qî +j -2k
Example 4; Find the angle between the vectors
A¯=2î +3ƒ +1k , B` =-4î +2ƒ -1k
منو يعرف يحل ذني الاسئله مالت الفيزياء
de between4md 8
agnitude 2 and vect
he angle a between
90, or 180.
following situations
must be. On each sit
an one correct answ
C , (c) A 8-6
B=30 betweenA"an
d the angle between t
N--4i +2 -1
دعاء صاحب حسین
4:19p äclul 21.02.04
II
Problem 1.19 Draw a circle in the xy plane. At a few representative points draw
the vector v tangent to the circle, pointing in the clockwise direction. By comparing
adjacent vectors, determine the sign of avx/ay and avy/ax. According to Eq. 1.41,
then, what is the direction of V x v? Explain how this example illustrates the geo-
metrical interpretation of the curl.
Chapter 1 Solutions
Classical Dynamics Of Particles And Systems
Ch. 1 - Prob. 1.1PCh. 1 - 1.2. Prove Equations 1.10 and 1.11 from...Ch. 1 - Prob. 1.3PCh. 1 - Show
(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1
Ch. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Consider a unit cube with one corner at the origin...Ch. 1 - Prob. 1.8PCh. 1 - For the two vectors
find
A − B and |A –...Ch. 1 - A particle moves in a plane elliptical orbit...
Ch. 1 - Prob. 1.11PCh. 1 - Let a, b, c be three constant vectors drawn from...Ch. 1 - X is an unknown vector satisfying the following...Ch. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - What surface is represented by r a = const, that...Ch. 1 - Obtain the cosine law of plane trigonometry by...Ch. 1 - Obtain the sine law of plane trigonometry by...Ch. 1 - Prob. 1.19PCh. 1 - 1-20. Show that
Ch. 1 - Show (see also Problem 1–11) that
Ch. 1 - Prob. 1.22PCh. 1 - Use the εijk notation and derive the identity
(A ×...Ch. 1 - Prob. 1.24PCh. 1 - Find the components of the acceleration vector a...Ch. 1 - Prob. 1.26PCh. 1 - If r and are both explicit functions of time,...Ch. 1 - Show that
Ch. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Show that
(a)
(b)
(c)
Ch. 1 - Show that (2arr+2brr)dt=ar2+br2+const. where r is...Ch. 1 - Show that (rrrrr2)dt=rr+C where C is a constant...Ch. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - A plane passes through the three points (x, y, z)...Ch. 1 - For what values of a are the vectors A = 2ai − 2j...
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