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(phys011)[2010](f)quiz~3224^_10044.pdf
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Quiz 5 - sol
1.
(a)
x(t) . xm cos(.t ..) v(t) . ..xm sin(.t ..) a(t) . ..2 xm cos(.t ..)
At t = 0,
x(0) . xmcos...0.085 (1) v(0) . ..xmsin...0.920 (2) a(0) . ..2 xmcos...47.0 (3)
a(0) 2
(3) . (1): . ..
x(0) a(0)
47.0 .
..
... . 23.5 rads 1 (ans)
x(0) . 0.0850
(b)
v(0) sin.
(2) . (1): ... ... tan.
x(0) cos.
v(0) . 0.920
tan... .. ..0.4603
.x(0) (23.51)(.0.085)
o oo
...24.7o or .. 180 . 24.7 . 155 x(0)
(1): x.m cos.
. 0.085 If . = .24.7o, x . ..0.094 m ..9.4 cm
mcos24.7o
. 0.085 If . = 155o, xm. o . 0.094 m . 9.4 cm
cos155
Since xm is positive, . = 155o and xm = 9.4 cm. (ans)
2.
Rotational inertia of the rod about the center
12
. Ia . ML
12

1 .... .(0.135)(0.124)2
.12 .
. 1.7298 .10.4 kgm2
Ia
Ib
Since T . 2.
and T . 2.
, we have
a
. b .
Ta
Ia
.
Tb Ib
Therefore, .Tb .2
I . I
b .
.
a
T
. a . .. 4.76 .2 .4 .42
..(1.73.10 ) . 6.12 .10 kgm (ans)
. 2.53 .