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Intuitively, angular momentum is the measure of how much the linear momentum is directed around an Origin. Since angular momentum depends upon the origin of choice, one must be carefule when discussing angular momentum to specify what origin and not to combine angular momenta about different origins. |
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In physics, angular momentum intuitively measures how much the linear momentum is directed around a certain point called the origin. Since angular momentum depends upon the origin of choice, one must be careful when discussing angular momentum to specify the origin and not to combine angular momenta about different origins. |
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L = r×p |
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:L = r×p |
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where L is angular momentum of the particle, r is the position of the particle expressed as a displacement vector, and p is the linear momentum of the particle. |
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where L is angular momentum of the particle, r is the position of the particle expressed as a displacement vector from the origin, and p is the linear momentum of the particle. If a systems consists of several particles, the total angular momentum about an origin can be gotten by adding (or integrating) all the angular momenta of the constituent particles. |
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L = |r||p|sinθ |
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:L = |r||p|sinθ |
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L = ±|p||rperpendicular| |
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:L = ±|p||rperpendicular| |
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L = ±|r||pperpendicular| |
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:L = ±|r||pperpendicular| |
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Remarkably, angular momentum is a [conserved quantity]? as long as there is no net Torque applied to the particle. What's more, this conservation can be generalized to a system of particles under most conditions so that: |
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In analogy to Newton's second law for linear momentum, we have the following law about angular momentum: |
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Lsystem = constant iff ∑τexternal = 0 |
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:dL/dt = τ where τ is the net torque about the origin. This implies that angular momentum is a [conserved quantity]? as long as there is no net torque applied to the particle. What's more, this conservation can be generalized to a system of particles under most conditions so that: :Lsystem = constant iff ∑τexternal = 0 |
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The conservation of angular momentum is used extensively in analyzing what is called central force motion. In central force motion, two bodies form an isolated system not influenced by outside forces, and the origin is placed somewhere on the line between the two bodies. Since any force the bodies exert on each other must be directed along this line, there can be no net torque, with respect to the afore-mentioned origin, on either body. Thus, angular momentum is conserved. Constant angular momentum is extremely useful when dealing with the orbits of planets and satelites, and also when analyzing the Bhor model of the atom. |
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The conservation of angular momentum is used extensively in analyzing what is called central force motion. In central force motion, two bodies form an isolated system not influenced by outside forces, and the origin is placed somewhere on the line between the two bodies. Since any force the bodies exert on each other must be directed along this line, there can be no net torque, with respect to the afore-mentioned origin, on either body. Thus, angular momentum is conserved. Constant angular momentum is extremely useful when dealing with the orbits of planets and satelites, and also when analyzing the Bohr model of the atom. |
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