Spherical Polar Coordinate System- physics II

It's specially for Electrical & Electronic Engineering, Computer Science & Engineering students for their second semister in first year.

2. Presented ByPresented By
Sonya Akter Rupa
ID-315161009
Department of CSE

3. Presented ToPresented To
Pro.Dr.Abu Zafor Ziauddin Ahamed
Lecturer of Physics
Hamdard University Bangladesh

4. (r, q)

5. •A coordinate system represents a point in the
plane by an ordered pair of numbers called
coordinates.
•Usually, we use Cartesian coordinates, which are
directed distances from two perpendicular axes.
•A coordinate system introduced by Newton, called
the polar coordinate system.
Polar Co-ordinate system

6. •We choose a point in the plane that is called the pole (or
origin) and is labeled O.
•Then, we draw a ray (half-line) starting at O called the polar
axis.
•If P is any other point in the plane, let
 r be the distance from O to P.
θ be the angle (usually measured in radians)
between the polar axis and the line OP.
Pole and Polar-axis

7. Plotting with a rectangular
coordinate system.
A new coordinate system
called the polar
coordinate system.

8. The center of the graph is
called the pole.
Angles are measured from
the positive x axis.
Points are
represented by a
radius and an angle

(r, q)
radius angle
To plot the point
÷
ø
ö
ç
è
æ
4
,5
p
First find the angle
Then move out along
the terminal side 5

9. CARTESIAN & POLAR COORDINATES
•If the point P has Cartesian Coordinates (x, y) and
polar coordinates (r, θ), then, from
the figure, we have:
cos sin
x y
r r
q q= =
Therefore,
cos
sin
x r
y r
q
q
=
=

10. Let's generalize this to find formulas for converting from
rectangular to polar coordinates.
(x, y)
r
q
y
x
222
ryx =+
x
y
=qtan
22
yxr +=
÷
ø
ö
ç
è
æ
=
-
x
y
1
tanq

11. Let's take a point in the rectangular coordinate system
and convert it to the polar coordinate system.
(3, 4)
r
q
Here, we can see how
to find r and q?
4
3
r = 5
222
43 r=+
3
4
tan=q
93.0
3
4
tan
1
=÷
ø
ö
ç
è
æ
=
-
q
We'll find q in radians
(5, 0.93)polar coordinates are:

12. Let's generalize the conversion from polar to rectangular
coordinates.
r
x
=qcos
( )q,r
r
y
x
q
r
y
=qsin
qcosrx=
qsinry=