Prove that the angular momentum of a system is constant in short
To prove that the angular momentum of a system is constant, we can make use of the conservation of angular momentum.
The angular momentum of a system is given by the equation:
L = Iω
Where L is the angular momentum, I is the moment of inertia of the system, and ω is the angular velocity.
If there are no external torques acting on the system (i.e., the system is isolated), then the total angular momentum of the system is conserved.
This can be mathematically expressed as:
L_initial = L_final
Or, I_initial ω_initial = I_final ω_final
Since the moment of inertia (I) depends on the mass distribution and geometry of the system, it remains constant unless there is a change in the system's mass distribution or geometry.
Similarly, if there are no external torques acting on the system, the angular velocity (ω) remains constant.
Therefore, if there are no external torques acting on the system, the angular momentum (L) of the system will remain constant.