Lecture 01
INTRODUCTION
PHY112
L 20
Course Logistics
Evaluations : Quizzes, Midsemester examination and Endsemester examination.
Section 1 [L-10] Tutor : Zahid Malik, FB-477, Office hours : Fridays 15:30 - 16:30
Section 2 [L-11] Tutor : Harshawardhan Wanare, FB-, Office hours : days 16:00-17:00
Section 3 [L-12] Tutor : Chanchal Sow, Southern Lab, LTE Unit, Office hours : Tuesdays 16:00-17:00
Section 4 [L-13] Tutor: Diptarka Das, RM-602, Office hours : Mondays 16:30 - 17:30
Tutor-in-residence : Amit Agarwal, FB-386, Office hours : Fridays 15:00 - 16:00
Theoretical physics
The aim is to find laws behind experiments / natural phenomena.
In the process we unify different classes.
Example : Electricity / Magnetism with Light
Example : Heat with Mechanics
The final goal is to find the smallest set of principles.
Classical dynamics
Ambitious goal : To predict the future of all particles and reconstruct
their past.
Wildly successful : Scattering of particles, motion of tides, orbits of
planets.
Single input : Force
Newton's framework
Force is an input.
Nature is kind, and there are only
some classes of forces.
Newton's framework
Nature is kind, and there are only
some classes of forces.
Many forces are special, and
when we analyze them
mathematically we discover new
principles.
Example : Energy conservation.
·
pi⃗ = mi r i⃗
·
⃗
F i = pi⃗
·
⃗
⃗
F i = F i( r,⃗ r)⃗
Newtonian dynamics
Assuming unit masses for simplicity
π/4
(1,0.1)
π/8
(0,0)
(1.1, − 1)
Newtonian dynamics
F ij⃗ =
⃗
F ext,1
1
2
3
rĵ − rî
2
rij
··
⃗ + F⃗ + F⃗
r 1⃗ = F 12
13
ext,1
⃗
F ext,1
1
2
3
⃗
F ext,2
··
⃗ + F⃗ + F⃗
r 1⃗ = F 12
13
ext,1
··
⃗ + F⃗ + F⃗
r 2⃗ = F 21
23
ext,2
··
⃗ + F⃗
r 3⃗ = F 31
32
Newtonian dynamics
x
4
3
2
1
0.5
-1
-2
-3
1.0
1.5
2.0
2.5
3.0
t
Newtonian dynamics
| r 1⃗ − r 2⃗ |
0.20
0.15
0.10
0.05
10
20
30
40
50
t
Despite success there is difficulty in the regimes of extremities
: tiny sizes, huge masses, and fast objects.
At tiny distances Quantum mechanics takes over.
ℏ→0
At fast speeds Special relativity takes over.
1/c → 0
At heavy masses General relativity takes over.
R→0
Despite success there is difficulty in the regimes of
extremities : tiny sizes, huge masses, and fast objects.
It is also difficult to explain dissipative systems, extended
objects, and many particles together using Newtonian
mechanics.
However, all developments are based on this. One can
build on Mathematics and make progress, drawing lessons
often from Nature and experiments.
Mathematical Preliminaries
Functions of many variables.
Partial derivatives.
Exact differentials.
Polar coordinates.
Gradient and derivatives in polar coordinates.
Matrices : Eigenvalues and eigenvectors.