Does angular momentum change with radius?
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Yes, angular momentum of a rotating body changes with radius.
Explanation:
The angular momentum
→
J
of a point mass
m
rotating with a linear velocity
→
v
at a radius
→
r
about an axis is given as
→
J
=
m
(
→
r
×
→
v
)
In scalar form, the angular momentum
J
of a point mass
m
rotating with an angular velocity
ω
at a radius
r
about an axis is given as
J
=
m
v
r
J
=
m
(
r
ω
)
r
J
=
m
r
2
ω
J
∝
r
2
The above equation shows that the angular momentum of a rotating body varies with the square of radius
r
.
In case of an extended body
r
is the distance of center of mass from the axis of rotation.
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