State the principle of conservation of angular momentum

Asked by admin @ 25/08/2021 in Physics viewed by 319 People

State and explain the principle of

conservation of angular momentum. Use a suitable illustration. Do we use it in our daily life? When?

Answered by admin @ 25/08/2021

The principle of Conservation of Angular Momentum states that in absence of any external torque there will not be any change of angular momentum of a body.

This means that , when no external torque acts on a body , the angular Momentum of the body along a particular axis remains conserved and doesn't change.

Mathematical Proof:

Torque on the system is zero

$\therefore \: \tau = 0$

$= > \dfrac{dL}{dt} = 0$

$= > dL = 0 \times dt$

$= > dL = 0$

$= > I \times d \omega = 0$

Integrating on both sides:

$\displaystyle= > I \times \int_{\omega_{1}}^{\omega_{2}} d \: \omega = \int \: 0 = 0$

$= > I\omega_{2} - I\omega_{1} = 0$

$= > I\omega_{2} = I\omega_{1}$

So angular momentum remains constant .

We use this principle in our daily life.

Dancers while rotating on their feet bring their arms towards their body so as to decrease the Moment Of Inertia. This leads to increased angular velocity and faster rotation.

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