Angular momentum for rotational motion about a fixed axis
`vecL=Ivecomega`
Differentiating w.r.t. time on both sides
`(dvecL)/(dt)=I(dvecomega)/(dt)`
`(dvecL)/(dt)=Ivecalpha` but `Ivecalpha=vectau`
`therefore (dvecL)/(dt)=vectau`, if the external torque is zero.
`(dvecL)/(dt)=0`
`therefore vecL` = constant
`therefore omega` is constant from `L=Iomega` [`because` I = constant]
Law of conservation of momentum : ..In the absence of resultant external torque the total angular momentum of a rigid body remains constant...
Illustration :
Suppose a girl seated on a swivel chair.
If chair rotate rapidly and girl stretch her arms in horizontal then the angular speed of chair and girl decreases and she folded her arms then her speed increase. This shown in figure.
Let this occurrence can be analyzed by angular moment. Suppose both arms is closer to the body, then moment of inertia is `I_(1)` and angular momentum is `omega_(1)` and when both hand are in horizontal, moment of inertia is `omega_(2)` and angular momentum is `omega_(2)`.
`therefore` According to the law of conservation of momentum
`I_(1)omega_(1)=I_(2)omega_(2)`
but `I_(1)ltI_(2)`
`therefore omega_(1)gtomega_(2)`
Moreover, this law are used by circus acrobat and diver.
Moreover, this law are also used by skaters and dancers performing a pirouette on the toes of one foot display .mastery. over this law.
