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Circ lar mo ion - Wikipedia
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Ci c la m
I
, ci c la m
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i n
i
,
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.T
-
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.
,
E
:
E
'
,
,
,
,
.
,
S
'
,
,
C
N
.W
.
'
,
e
Uniform circular motion
F m la
I
la c di a e
U i g c m le
mbe
Vel ci
Rela i i ic ci c la m i
Accele a i
Non-uniform
Applications
See also
References
External links
U if
ci c la
I
,
i
if m ci c la m
.S
.T
,
i
,
'
,
:
'
,
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;
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,
,
.
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Circ lar mo ion - Wikipedia
I
,
,
.
Formulas
F
I
r,
T,
,
C = 2 r.
,
:
a d he
i
a e adia
T
/ ec
:
T
d
Figure 1: Velocity and
acceleration a in uniform
circular motion at angular
rate ; the speed is constant,
but the velocity is always
tangent to the orbit; the
acceleration has constant
magnitude, but always points
toward the center of rotation.
t :
T
, α,
I
:
,
.
T
:
T
:
T
F
-
= d / dt. T
. W
1. T
Figure 2: The velocity vectors at time t
and time t + dt are moved from the orbit
on the left to new positions where their
tails coincide, on the right. Because the
velocity is xed in magnitude at = r ,
the velocity vectors also sweep out a
circular path at angular rate . As dt
0,
the acceleration vector a becomes
perpendicular to , which means it points
toward the center of the orbit in the circle
on the left. Angle dt is the very small
angle between the two velocities and
tends to zero as dt 0.
,
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Circ lar mo ion - Wikipedia
,
=
(t).[1]
2
(t),
,
r. L
(t)
r
I
,
.
C
Figure 3: (Left) Ball in circular motion rope
provides centripetal force to keep ball in circle
(Right) Rope is cut and ball continues in straight
line with velocity at the time of cutting the rope, in
accord with Newton's law of inertia, because
centripetal force is no longer there.
,
,
.
The eed i 1 me e e ec d.
The i a d accele a i i 1 me e e
ae
2
ec d, / .
I i
bjec
a ce i e al f ce f 1 kil g am me e
e
a e ec d, hich i
e e
.
The m me m f he b d i 1 kg m 1.
The m me
f i e ia i 1 kg m2.
The a g la m me m i 1 kg m2 1.
The ki e ic e e g i 1 j le.
The ci c mfe e ce f he bi i 2 ( 6.283) me e .
The e i d f he m i i 2 ec d e
.
The f e
e c i (2 )
1
he
Figure 1: Vector relationships for uniform
circular motion; vector representing the
rotation is normal to the plane of the orbit.
.
In polar coordinates
D
R
,
.S
F
4. T
(t)
vector
:
t
.I
,
.I
.
T
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Circ lar mo ion - Wikipedia
B
,
.T
,
,
. I
d
dt,
,
d . S
4. H
:
F
( ,
Figure 4: Polar coordinates for circular trajectory. On the
left is a unit circle showing the changes
and
in
the unit vectors
and
for a small increment
in
angle .
,
)
.T
,
d
.H
:
T
.T
:
T
.A
/2 + . H
,
,
d ,
d
,
:
. (O
C
,
decrease
:
T
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,
d .) S
,
F
4.
:
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Circ lar mo ion - Wikipedia
:
Using complex numbers
C
.L
.T
x
,
i
"
":
,
S
, t.
:
dot
.
W
:
:
T
,
.
Velocity
F
1
.B
,
A
speed,
a,
direction
(
. T
r,
. T
)
,
(
.
.T
F
s=r .T
.
)
,
,
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Circ lar mo ion - Wikipedia
. (B
,
= v/r.) T
,v
v,
,
.
Relativistic circular motion
I
-
-
,
,
,
,
,
,
-
,
:
Acceleration
T
-
F
2
.O
,
. B
.F
,
d =
dt
v d ,
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Centripetal acceleration for some values of radius and magnitude of velocity
1 /
3.6
/
2.2
v
r
S
2 /
7.2
/
4.5
5
18
11
a
/
10
36
22
/
/
/
B
20
72
45
/
/
C
a
50
180
110
/
/
100
360
220
A
/
/
ba
10 m/s2
1.0 g
40 m/s2
4.1 g
250 m/s2
25 g
1.0 km/s2
100 g
4.0 km/s2
410 g
25 km/s2
2500 g
100 km/s2
10000 g
20
7.9
5.0 m/s2
0.51 g
20 m/s2
2.0 g
130 m/s2
13 g
500 m/s2
51 g
2.0 km/s2
200 g
13 km/s2
1300 g
50 km/s2
5100 g
50
1.6
2.0 m/s2
0.20 g
8.0 m/s2
0.82 g
50 m/s2
5.1 g
200 m/s2
20 g
800 m/s2
82 g
5.0 km/s2
510 g
20 km/s2
2000 g
1.0 m/s2
0.10 g
4.0 m/s2
0.41 g
25 m/s2
2.5 g
100 m/s2
10 g
400 m/s2
41 g
2.5 km/s2
250 g
10 km/s2
1000 g
2
6.6
500 mm/s2
0.051 g
2.0 m/s2
0.20 g
13 m/s2
1.3 g
50 m/s2
5.1 g
200 m/s2
20 g
1.3 km/s2
130 g
5.0 km/s2
510 g
5
16
200 mm/s2
0.020 g
800 mm/s2
0.082 g
5.0 m/s2
0.51 g
20 m/s2
2.0 g
80 m/s2
8.2 g
500 m/s2
51 g
2.0 km/s2
200 g
100 mm/s2
0.010 g
400 mm/s2
0.041 g
2.5 m/s2
0.25 g
10 m/s2
1.0 g
40 m/s2
4.1 g
250 m/s2
25 g
1.0 km/s2
100 g
20
66
50 mm/s2
0.0051 g
200 mm/s2
0.020 g
1.3 m/s2
0.13 g
5.0 m/s2
0.51 g
20 m/s2
2g
130 m/s2
13 g
500 m/s2
51 g
50
160
20 mm/s2
0.0020 g
80 mm/s2
0.0082 g
500 mm/s2
0.051 g
2.0 m/s2
0.20 g
8.0 m/s2
0.82 g
50 m/s2
5.1 g
200 m/s2
20 g
10 mm/s2
0.0010 g
40 mm/s2
0.0041 g
250 mm/s2
0.025 g
1.0 m/s2
0.10 g
4.0 m/s2
0.41 g
25 m/s2
2.5 g
100 m/s2
10 g
200
660
5.0 mm/s2
0.00051 g
20 mm/s2
0.0020 g
130 m/s2
0.013 g
500 mm/s2
0.051 g
2.0 m/s2
0.20 g
13 m/s2
1.3 g
50 m/s2
5.1 g
500
1600
2.0 mm/s2
0.00020 g
8.0 mm/s2
0.00082 g
50 mm/s2
0.0051 g
200 mm/s2
0.020 g
800 mm/s2
0.082 g
5.0 m/s2
0.51 g
20 m/s2
2.0 g
1.0 mm/s2
0.00010 g
4.0 mm/s2
0.00041 g
25 mm/s2
0.0025 g
100 mm/s2
0.010 g
400 mm/s2
0.041 g
2.5 m/s2
0.25 g
10 m/s2
1.0 g
10
3.9
Lab a
1
3.3
Pa
a
10
33
R
- a
a
100
330
F
a
-a
1
3300
H
a
N
-
I
-
a
if
if
m ci c la m
i
. S
,
.
I
-
( )
,
(
). T
:
. U
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Circ lar mo ion - Wikipedia
I
-
,
. H
.
T
.T
. T
). T
(W
)
(
.
I
-
,
. B
,
.F
.I
,
'
'
,
.T
.T
(
. H
)
,
.F
,
. A
,
,
'
.
T
.T
.O
,
'
.T
,
.T
N
,
.W
'
'
,
.
A
. F
.[2]
A
,
lica i
S
-
. W
,
.I
,
-
-
.A
,
.
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Circ lar mo ion - Wikipedia
R
. T
.T
.S
,
.
U
,
.A
,
(
,
,
,
.). F
,
,
,
.
I
,
.D
,
.T
,
.
R
.T
:
.T
;
,
C
,
.
See al
A g la m me m
E ai
f m i f ci c la m i
E am le: ci c la m i
Fic i i
f ce
Ge a i a
bi
Ge
ch
bi
Pe d l m (ma hema ic )
Reac i e ce if gal f ce
Reci ca i g m i
Sim le ha m ic m i #U if m ci c la m i
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Circ lar mo ion - Wikipedia
Sli g ( ea
)
Refe e ce
1. K d e , Je M.; Hj h, P l G. (2000). Ele e
f Ne
ia
echa ic : i cl di g
li ea
d a ic (h
://b k .g gle.c m/b k ?id=U m
_lWUC) (3 ed.). S i ge . . 96. ISBN 3540-67652-X., Cha e 5 age 96 (h
://b k .g gle.c m/b k ?id=U m
_lWUC& g=PA96)
2. G me , R W; He a de -G me , J J; Ma i a, V (25 J l 2012). "A j m i g c li de
a i cli ed
la e" (h
://
. e ea chga e. e / blica i /236030807). E . J. Ph . IOP. 33 (5): 1359 1365.
a Xi :1204.0600 (h
://a i . g/ab /1204.0600). Bibc de:2012EJPh...33.1359G (h
:// i.ad ab .
ha a d.ed /ab /2012EJPh...33.1359G). d i:10.1088/0143-0807/33/5/1359 (h
://d i. g/10.1088%
2F0143-0807%2F33%2F5%2F1359). S2CID 55442794 (h
://a i. ema ic ch la . g/C
ID:55
442794). Re ie ed 25 A il 2016.
E e
al li k
Ph cli : Mecha ic i h a ima i
a d ide cli (h
:// eb.a chi e. g/ eb/20070601020244/
h ://
. h cli .
.ed .a /) f m he U i e i
f Ne S h Wale
Ci c la M i (h ://
.ligh a dma e .c m/h ml_b k /1 /ch09/ch09.h ml) a cha e f m a
li e e b k
Ci c la M i Lec e (h
:// eb.a chi e. g/ eb/20100117190656/h :// c .mi .ed /Oc Web/P
h ic /8-01Ph ic -IFall1999/Vide Lec e /de ail/embed05.h m) a ide lec e
CM
[1] (h
://
.ama
.c m/U i e-Pe ce i
-Ph ic -C mme a ie - l i
/d /1542776058)
a
li e e b k i h diffe e a al i f ci c la m i
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T
a
a
a
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