An uniform rod of length 'L' is rotating with a constant angular velocity omega about an axis passing through its one end and perpendicular to its length.If its rotational kinetic energy is K then find the mass'M'of the rod.
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Answer:
dT=dm(l-x)ω2
dT=
m
l
dx(l-x)ω2
⇒∫
T
0
dT=∫
l/2
0
mω2
l
(l0x)dx
mω2
l
[lx-
x2
2
]
l/2
0
=
mω2
l
[
l2
2
-
l2
g
]
∴ Tension at mid point is:
T=
3
8
mlω2⇒ stress =
3mlω2
8A
⇒ strain
3mlω2
8AY
Alternatively Tension at mid point can be found by using
Fext=macm
T=
m
2
(ω2
3l
4
)=
3
8
mω2l
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