INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 1
29.8.2007
A two-dimensional autonomous dynamical system in continuous time is specied
by a pair of real variables x and y whose time evolution is specied by
Chapter 4
Oscillations
In this chapter we will discuss oscillatory motion. The simplest examples of such
motion are a swinging pendulum and a mass on a spring, but it is possible to make
a system more complicated by introducing a damping force and/or an e
Chapter 5
Conservation of energy and
momentum
Conservation laws are extremely important in physics. They are enormously
helpful, both quantitatively and qualitatively, in figuring out what is going on in
a physical system. When we say that something is co
148
Conservation of energy and momentum
V(x)
Example: A particle moves under the influence of the potential V (x) =
A/x2 B/x, where A, B > 0. Find the frequency of small oscillations around the
equilibrium point. This potential is relevant to planetary mo
Cylindrical Polar Co-ordinates (,z)
r
Position vector is r = e + z e z
r
d r = d e + d e + dz e z
r
v = & e + & e + z&e z
r
& & + &)e + &
a =(& & 2 ) e + (2
z e z
z
P
z
x
dz d
d
Area Vector
r
r
r
Az = dr dr = d d ez
r
r
r
A = drz dr = dzd e
r
r
r
A = dr
DEPARTMENT OF PHYSICS
INDIAN INSTITUTE OF TECHNOLOGY, MADRAS
PH101 Physics I
18.10.2002
Particle Motion in a Central Force
Contents: Particle kinematics in cylindrical and spherical polar coordinates;
motion under a central force; conservation of angular
35
Physics I Course Material
y
ey
e
e
P
A new basis of unit vectors (
e , e ) is defined along the directions of increasing and
increasing respectively. From Fig. 6.2, it
is obvious that
ex
e = cos ex + sin ey ,
e = sin ex + cos ey . (6.6)
x
O
The inverse
11/20/2013
Recap: Gradient
Vector field from Scalar fields
The gradient of a scalar function at any point indicates the
direction In which the function has largest rate of increase
Note: Not every vector field needs to be a gradient of a scalar field
Scal
5.9 Problems
5.9
173
Problems
Section 5.1 Conservation of energy in one dimension
5.1. Minimum length *
The shortest configuration of string joining three given points is the one
shown in the first setup in Fig. 5.19, where all three angles are 120 . 24
E
INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 4
17.10.2007
1. (a) The probability density of the xcomponent of the velocity of a molecule
of mass m in a classical ideal gas is
1/2
m
2kB T
exp
2
mvx
2kB T
.
INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 3
12.9.2007
1. We have seen that canonical transformations (CTs) are symplectic transformations in the following sense. Let x = (q , p) where q and p stand for
INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 2
1.9.2007
1. Indicate whether the statements in quotation marks are true or false.
(a) The Lagrangian of a particle moving in a central potential V (r) has tw
NPTEL COURSE ON CLASSICAL PHYSICS
V. Balakrishnan
Department of Physics, Indian Institute of Technology Madras
Chennai 600 036, India
Two-dimensional Autonomous Dynamical Systems
A two-dimensional (2D) autonomous dynamical system in continuous time is spe
684
Appendix B
B.4 Gradient
Given a function f (x, y, z) (well work mainly with three variables from now on),
we can form the vector whose components are the partial derivatives of f , namely
(f /x, f /y, f /z). This vector is called the gradient. If we d