CLASSICAL DYNAMICS OF PARTICLES AND SYST
5th Edition
ISBN: 9780357670675
Author: Thornton
Publisher: CENGAGE L
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Chapter 1, Problem 1.38P
To determine
The value of the integral
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Let vectors A⃗=(2,−4)
A
→
=
(
2
,
−
4
)
and B⃗=(−3,1)
B
→
=
(
−
3
,
1
)
.
Calculate the following:
What is the angle θAB
θ
A
B
between A⃗
A
→
and B⃗
B
→
?
Express the vector field D = (x²+y²)⁻¹ (X2x + Y2y) in cylindrical components and cylindrical variables.
An alternative line definition Given a fxed point P,(xo- Yo)
and a nonzero vector n = (a, b), the set of points P(x, y) for which
PP is orthogonal to n is a line e (see figure). The vector n is called a
normal vector or a vector normal to e.
yA
n = (a, b)
P(x, y)
Suppose a line is normal to n = (5, 3). What is the slope of
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Chapter 1 Solutions
CLASSICAL DYNAMICS OF PARTICLES AND SYST
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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