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WHAT IS CONSERVATION OF ANGULAR MOMENTUM?

WHAT IS CONSERVATION OF ANGULAR MOMENTUM?

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Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
9 years ago
The law of conservation of angular momentum states that when no external torque acts on an object or a closed system of objects, no change of angular momentum can occur. Hence, the angular momentum before an event involving only internal torques or no torques is equal to the angular momentum after the event. This conservation law mathematically follows from isotropy, or continuous directional symmetry of space (no direction in space is any different from any other direction).

The time derivative of angular momentum is called torque:
\tau =\frac{\mathrm{d} L}{\mathrm{d} t}=\frac{\mathrm{d} r}{\mathrm{d} t}\times p+r\times \frac{\mathrm{d} p}{\mathrm{d} t}=0+r\times F=r\times F

(The cross-product of velocity and momentum is zero, because these vectors are parallel.) So requiring the system to be "closed" here is mathematically equivalent to zero external torque acting on the system:
L_{system}=constant\leftrightarrow \sum \tau _{ext}=0

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