11) State and Prove Principle of conservation of angular momentum, give SI unit of angular momentum
Answers
Answer:
Let
L
be the angular momentum.
It is the vector product of radius vector and linear momentum.
r
×
p
Please note that you should not say it as a product of linear momentum and radius vector, because vector product is not commutative.
Rate of change of
L
with respect to time t is given by
dt
d
L
=
dt
d(
r
×
p
)
=(
r
×
dt
d
p
)+(
p
×
dt
d
r
)
=(
r
×
F
)+(
p
×
V
) ∵ rate of change of linear momentum is force and rate of change of radius vector is velocity.
∴
dt
d
L
=
τ
+m(
V
×
V
) here
r
×
F
= torque ,
p
=m
v
∴
dt
d
L
=
τ
cross product of any vector with itself is zero.
∴ if τ=0 then
dt
d
L
This means that in the absence of any external torque, the total angular momentum of a rotating body is conserved.
This can be mathematically written as I
1
ω
1
=I
2
ω
2
if τ=0
Here I is moment of inertia and ω is angular velocity.
We know that Iω=L
Answer: