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19.8: Principle of Conservation of Angular Momentum
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Dourmashkin)/19%3A_Angular_Momentum/19.08%3A_Principle_of_Conservation_of_Angular_Momentum
Principle of Conservation of Angular Momentum argues that if the external torque acting on a system is zero, then the angular momentum of the system is constant. So for any change of state of the syst...Principle of Conservation of Angular Momentum argues that if the external torque acting on a system is zero, then the angular momentum of the system is constant. So for any change of state of the system the change in angular momentum is zero
6.3: Examples
https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/06%3A_C6)_Conservation_of_Angular_Momentum_I/6.03%3A_Examples
In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the ...In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the angular velocity must increase to conserve angular momentum. Systems containing both point particles and rigid bodies can be analyzed using conservation of angular momentum. The angular momentum of all bodies in the system must be taken about a common axis.
47.2: Conservation of Angular Momentum
https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/47%3A_Angular_Momentum/47.02%3A_Conservation_of_Angular_Momentum
Angular momentum, like linear momentum, is a conserved vector quantity: in a closed system (in which no angular momentum enters or leaves the system), the total angular momentum is constant. In a clos...Angular momentum, like linear momentum, is a conserved vector quantity: in a closed system (in which no angular momentum enters or leaves the system), the total angular momentum is constant. In a closed system, angular momentum may be transferred from one body to another, but the total angular momentum - the sum of the angular momenta of all bodies in the system — will remain constant.
5A: Conservation of Angular Momentum
https://phys.libretexts.org/Bookshelves/University_Physics/Calculus-Based_Physics_(Schnick)/Volume_A%3A_Kinetics_Statics_and_Thermodynamics/05A%3A_Conservation_of_Angular_Momentum
The angular momentum of an object is a measure of how difficult it is to stop that object from spinning. For an object rotating about a fixed axis, the angular momentum depends on how fast the object ...The angular momentum of an object is a measure of how difficult it is to stop that object from spinning. For an object rotating about a fixed axis, the angular momentum depends on how fast the object is spinning, and on the object's rotational inertia (also known as moment of inertia) with respect to that axis.
11.4: Conservation of Angular Momentum
https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/11%3A__Angular_Momentum/11.04%3A_Conservation_of_Angular_Momentum
In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the ...In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the angular velocity must increase to conserve angular momentum. Systems containing both point particles and rigid bodies can be analyzed using conservation of angular momentum. The angular momentum of all bodies in the system must be taken about a common axis.
2.5.E: Conservation of Angular Momentum (Exercises)
https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/02%3A_Book-_Conceptual_Physics_(Crowell)/2.05%3A_Conservation_of_Angular_Momentum/2.5.E%3A_Conservation_of_Angular_Momentum_(Exercises)
Note that because the $x$ , $y$ , and $z$ components are treated symmetrically in the definitions of the vector cross product, it is only necessary to carry out the proof for the $x$ component o...Note that because the $x$ , $y$ , and $z$ components are treated symmetrically in the definitions of the vector cross product, it is only necessary to carry out the proof for the $x$ component of the result. (b) Applying this to the angular momentum of a rigidly rotating body, $L=\int \mathbf{r}\times(\boldsymbol{\omega}\times\mathbf{r})dm$ , show that the diagonal elements of the moment of inertia tensor can be expressed as, e.g., $I_{xx}=\int (y^2+z^2)dm$ . (c) Find the diagonal eleme…
10.5: Angular Momentum and Its Conservation
https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/10%3A_Rotational_Motion_and_Angular_Momentum/10.05%3A_Angular_Momentum_and_Its_Conservation
Angular momentum is completely analogous to linear momentum. It has the same implications in terms of carrying rotation forward, and it is conserved when the net external torque is zero. Angular momen...Angular momentum is completely analogous to linear momentum. It has the same implications in terms of carrying rotation forward, and it is conserved when the net external torque is zero. Angular momentum, like linear momentum, is also a property of the atoms and subatomic particles.
5.E: Conservation of Angular Momentum (Exercises)
https://phys.libretexts.org/Bookshelves/Conceptual_Physics/Conceptual_Physics_(Crowell)/05%3A_Conservation_of_Angular_Momentum/5.E%3A_Conservation_of_Angular_Momentum_(Exercises)
Note that because the $x$ , $y$ , and $z$ components are treated symmetrically in the definitions of the vector cross product, it is only necessary to carry out the proof for the $x$ component o...Note that because the $x$ , $y$ , and $z$ components are treated symmetrically in the definitions of the vector cross product, it is only necessary to carry out the proof for the $x$ component of the result. (b) Applying this to the angular momentum of a rigidly rotating body, $L=\int \mathbf{r}\times(\boldsymbol{\omega}\times\mathbf{r})dm$ , show that the diagonal elements of the moment of inertia tensor can be expressed as, e.g., $I_{xx}=\int (y^2+z^2)dm$ . (c) Find the diagonal eleme…
4.5.2: Conservation of Angular Momentum
https://phys.libretexts.org/Workbench/PH_245_Textbook_V2/04%3A_Module_3_-_Conservation_Laws/4.05%3A_Objective_3.e./4.5.02%3A_Conservation_of_Angular_Momentum
In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the ...In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the angular velocity must increase to conserve angular momentum. Systems containing both point particles and rigid bodies can be analyzed using conservation of angular momentum. The angular momentum of all bodies in the system must be taken about a common axis.
10.10: Conservation of Angular Momentum
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/10%3A_Momentum/10.10%3A_Conservation_of_Angular_Momentum
The final kinetic energy is $\frac{1}{2} (4I_{0}) \omega^{2} = \frac{1}{2} (4I_{0}) \left(\dfrac{\omega_{0}}{4}\right)^{2} = \frac{1}{8} I_{0} \omega_{0}^{2}. \nonumber$ Therefore, the ratio of the ...The final kinetic energy is $\frac{1}{2} (4I_{0}) \omega^{2} = \frac{1}{2} (4I_{0}) \left(\dfrac{\omega_{0}}{4}\right)^{2} = \frac{1}{8} I_{0} \omega_{0}^{2}. \nonumber$ Therefore, the ratio of the final kinetic energy to the initial kinetic energy is $\frac{\frac{1}{8} I_{0} \omega_{0}^{2}}{\frac{1}{2} I_{0} \omega_{0}^{2}} = \frac{1}{4} \ldotp \nonumber$ Thus, 3/4 of the initial kinetic energy is lost to the coupling of the two flywheels.
12.4: Conservation of Angular Momentum
https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/12%3A__Angular_Momentum/12.04%3A_Conservation_of_Angular_Momentum
In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the ...In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the angular velocity must increase to conserve angular momentum. Systems containing both point particles and rigid bodies can be analyzed using conservation of angular momentum. The angular momentum of all bodies in the system must be taken about a common axis.

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