The particle travel on the semicircular path of radius r,the magnitude of particle is
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The distance D, that is the length of the actual path covered by the particle(0A'ABC) as shown in Fig.
D = length of the semicircle OA'A + length AB + length BC. This gives D = πR + R +
2R = (π + 3)R.
Since OA = 2R,AB = R, and BC = 2R, the coordinates of C can be given as C = (2R, R,2R). Then the position of C is expressed as:
r
c
= 2R
i
^
+ R
j
^
+ 2R
k
^
As
s
(=
OC
) =
r
c
-
r
0
, substituting
r
c
and
r
0
= 0
i
^
+0
j
^
+0
k
^
,
we obtain
s
= (2
i
^
+
j
^
+ 2
k
^
)R.
Its magnitude |
s
| = (
2
1
+1
2
+2
2
R = 3R
Hence,
s
D
=
3R
(π+3)R
=
3
π+3
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