Lecture_1________________________pptx.pdf

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NikhilKumarJaiswal2

Ghhjnnn

Devices & Hardware

Highlights of the course
Co-ordinate Systems
Introduction to Vector
Operators
Work , Energy and Conservation laws
Rigid body in motion
Oscillations and Waves
Quantum Physics
RKE_JJ_PH103_2021 1

Introduction to
DIFFERENT CO-ORDINATE SYSTEMS
INFINITESIMAL LINE, AREA AND VOLUME ELEMENTS
Co-ordinate Systems
2
RKE_JJ_PH103_2021
Chapter 1

Outline
Choice of Co-ordinate systems
Cartesian Co-ordinates: Unit vectors, Infinitesimal line, area and
volume element
Plane-Polar Co-ordinates: Unit vectors, transformations, Rate of
change, velocity and acceleration, Infinitesimal line, area
element
Cylindrical Co-ordinates: Unit vectors and its transformations,
Rate of change, velocity and acceleration, Infinitesimal line, area
and volume element
Spherical Polar Co-ordinates: Unit vectors and its
transformations, Rate of change, velocity and acceleration,
Infinitesimal line, area and volume element
RKE_JJ_PH103_2021 3

Why do we need different coordinate
system?
4
RKE_JJ_PH103_2021

Why do we need different coordinate
system?
X Y
1 0
0.9397 0.34201
0.76606 0.64277
0.50003 0.86601
0 1
r
1 0
1 20
1 40
1 60
1 90
Proper choice of a
coordinate system can
vastly simplify a problem 5
RKE_JJ_PH103_2021
r

Representing a vector in Cartesian
Co-ordinate system
RKE_JJ_PH103_2021 6

A coordinate system consists of four basic elements:
1) Choice of origin (2) Choice of axes (3) Choice of positive direction for each axis (4)
Choice of unit vectors for each axis
7
RKE_JJ_PH103_2021
Cartesian Co-ordinates

Infinitesimal (very small) line element
in Cartesian Co-ordinate system
RKE_JJ_PH103_2021 8

Infinitesimal line element
9
RKE_JJ_PH103_2021
Cartesian Co-ordinates
x
y
z

RKE_JJ_PH103_2021 10
Infinitesimal Area element in
Cartesian Co-ordinate system

Cartesian Co-ordinates
Infinitesimal Area element
11
RKE_JJ_PH103_2021
x
y
z
dx
dz

Infinitesimal Volume element in
Cartesian Co-ordinate system
RKE_JJ_PH103_2021 12

Cartesian Coordinates
Infinitesimal Volume element
13
RKE_JJ_PH103_2021
x
y
z

Polar co-ordinate system
RKE_JJ_PH103_2021 14

Representation of a vector and unit
vector transformations in polar
co-ordinates
RKE_JJ_PH103_2021 15

Representation of a Vector in Polar
Coordinates
RKE_JJ_PH103_2021 16
X
Y
r
What is unit vector

Unit vector representation in Polar Coordinates
X
Y
(x,y) ex
ey
r
er
17
RKE_JJ_PH103_2021
Verify that = 0
Above vector in Polar Co-ordinates is
represented as
What is and in terms of and ?
er ex
ey
What is and in terms of and ?
er
ex
ey
-ex

Motion in polar co-ordinates, velocity and
acceleration
RKE_JJ_PH103_2021 18

Motion in Plane Polar Coordinates
X
Y
(x1
,y1
) ex
ey
r1
er
(x2
,y2
)
ex
ey
r2
er
Cartesian coordinate system: Constant unit vectors
Plane polar coordinate system: Varying unit vectors
19
RKE_JJ_PH103_2021

Velocity and acceleration in polar
co-ordinates
RKE_JJ_PH103_2021 20

Velocity in Polar Coordinates
Velocity in Cartesian Coordinates:
?
?
21
RKE_JJ_PH103_2021
Velocity in Polar Coordinates:

Through a geometrical consideration
X
Y
(x1,y1)
r1
er1
(x2,y2)
r2
er2
-er1
22
RKE_JJ_PH103_2021

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Lecture_1________________________pptx.pdf

1. Highlights of the course Co-ordinate Systems Introduction to Vector Operators Work , Energy and Conservation laws Rigid body in motion Oscillations and Waves Quantum Physics RKE_JJ_PH103_2021 1

2. Introduction to DIFFERENT CO-ORDINATE SYSTEMS INFINITESIMAL LINE, AREA AND VOLUME ELEMENTS Co-ordinate Systems 2 RKE_JJ_PH103_2021 Chapter 1

3. Outline Choice of Co-ordinate systems Cartesian Co-ordinates: Unit vectors, Infinitesimal line, area and volume element Plane-Polar Co-ordinates: Unit vectors, transformations, Rate of change, velocity and acceleration, Infinitesimal line, area element Cylindrical Co-ordinates: Unit vectors and its transformations, Rate of change, velocity and acceleration, Infinitesimal line, area and volume element Spherical Polar Co-ordinates: Unit vectors and its transformations, Rate of change, velocity and acceleration, Infinitesimal line, area and volume element RKE_JJ_PH103_2021 3

4. Why do we need different coordinate system? 4 RKE_JJ_PH103_2021

5. Why do we need different coordinate system? X Y 1 0 0.9397 0.34201 0.76606 0.64277 0.50003 0.86601 0 1 r 1 0 1 20 1 40 1 60 1 90 Proper choice of a coordinate system can vastly simplify a problem 5 RKE_JJ_PH103_2021 r

6. Representing a vector in Cartesian Co-ordinate system RKE_JJ_PH103_2021 6

7. A coordinate system consists of four basic elements: 1) Choice of origin (2) Choice of axes (3) Choice of positive direction for each axis (4) Choice of unit vectors for each axis 7 RKE_JJ_PH103_2021 Cartesian Co-ordinates

8. Infinitesimal (very small) line element in Cartesian Co-ordinate system RKE_JJ_PH103_2021 8

9. Infinitesimal line element 9 RKE_JJ_PH103_2021 Cartesian Co-ordinates x y z

10. RKE_JJ_PH103_2021 10 Infinitesimal Area element in Cartesian Co-ordinate system

11. Cartesian Co-ordinates Infinitesimal Area element 11 RKE_JJ_PH103_2021 x y z dx dz

12. Infinitesimal Volume element in Cartesian Co-ordinate system RKE_JJ_PH103_2021 12

13. Cartesian Coordinates Infinitesimal Volume element 13 RKE_JJ_PH103_2021 x y z

14. Polar co-ordinate system RKE_JJ_PH103_2021 14

15. Representation of a vector and unit vector transformations in polar co-ordinates RKE_JJ_PH103_2021 15

16. Representation of a Vector in Polar Coordinates RKE_JJ_PH103_2021 16 X Y r What is unit vector

17. Unit vector representation in Polar Coordinates X Y (x,y) ex ey r er 17 RKE_JJ_PH103_2021 Verify that = 0 Above vector in Polar Co-ordinates is represented as What is and in terms of and ? er ex ey What is and in terms of and ? er ex ey -ex

18. Motion in polar co-ordinates, velocity and acceleration RKE_JJ_PH103_2021 18

19. Motion in Plane Polar Coordinates X Y (x1 ,y1 ) ex ey r1 er (x2 ,y2 ) ex ey r2 er Cartesian coordinate system: Constant unit vectors Plane polar coordinate system: Varying unit vectors 19 RKE_JJ_PH103_2021

20. Velocity and acceleration in polar co-ordinates RKE_JJ_PH103_2021 20

21. Velocity in Polar Coordinates Velocity in Cartesian Coordinates: ? ? 21 RKE_JJ_PH103_2021 Velocity in Polar Coordinates:

22. Through a geometrical consideration X Y (x1,y1) r1 er1 (x2,y2) r2 er2 -er1 22 RKE_JJ_PH103_2021

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