Momentum Conservation
Conservation of momentum is a fundamental conservation law of physics. It states that the momentum of a system is constant if there are no external forces acting on the system.
In physics, conservation laws state that, in a closed system, the total quantity of momentum of the system remains constant; that is, its rate of change is zero. Mathematically, this is expressed as dX/dt = 0 for a scalar quantity X, and as div F = 0 for a vector quantity F. The most well-known conservation law is the law of conservation of energy, which states that the total energy of a closed system remains constant during a transformation. This is the first law of thermodynamics, and can also be stated as the total energy of a closed system is equal to the sum of its potential and kinetic energies. Another conservation law, for which no exception has yet been recorded, is that the total electric charge of a closed system remains constant. Another example is the law of conservation of mass-energy expressed by German-American physicist Albert Einstein as E = mc2 in his special relativity theory, which states that the total energy of a particle (E) has a mass (m) equal to E/c2 , or the total mass of a particle has an energy equal to mc2 .
Conservation of momentum is implicit in English physicist and mathematician Sir Isaac Newton's first law of motion, the law of inertia, which holds that a body at constant velocity (including a velocity of zero relative to a particular reference frame) will remain at constant velocity unless acted upon by an external force. Conservation of momentum applies to both linear and angular momentum. For translational or straight-line motion, the linear momentum vector is defined as the product of the mass of a particle and its velocity: p = mv. For rotational motion, the angular momentum vector is defined as the product of the moment of inertia of the particle and its angular velocity: L = I. Conservation of linear momentum states that the total linear momentum (p) of a closed system is always conserved when there is no net acting force and conservation of angular momentum similarly states that the total angular momentum (L) of a closed system is always conserved when there is no net torque. This is also implicit in Newton's third law, or force-pair law, which states that whenever a body exerts a force on another body, the latter exerts a force of equal magnitude and opposite direction on the former. Therefore, the rate of change of momentum of the first body is equal and opposite to that of the second body, and the total rate of change of momentum in the system is zero, which is equivalent to stating that the momentum of the system is conserved.
Conservation of angular momentum is the underlying principle of the gyroscope, an instrument consisting of a rapidly spinning wheel set in a framework allowing the wheel to tilt in any direction which prevents the occurrence of a net torque. Thus, the axis of rotation points in a fixed direction, and the angular velocity and momentum does not change. No matter how the gyroscope is turned, it will always point in the same direction because no torque is exerted to change it.
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