Linear Momentum of a System of Particles
In classical mechanics, momentum (pl. momenta; SI unit kg•m/s, or, equivalently, N•s) is the product of the mass and velocity of an object (p = mv). In relativistic mechanics, this quantity is multiplied by the Lorentz factor. Momentum is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector quantity, since it has a direction as well as a magnitude. Angular momentum is a pseudovector quantity because it gains an additional sign flip under an improper rotation. The total momentum of any group of objects remains the same unless outside forces act on the objects (law of conservation of momentum).
Momentum is a conserved quantity, meaning that the total momentum of any closed system (one not affected by external forces) cannot change. Although originally seen to be due to Newton's laws, this law is also true in special relativity, and with appropriate definitions a (generalized) momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity. I like to share this Linear Accelerator with you all through my article.
We have briefly defined linear momentum, while describing Newton's second law of motion. The law defines force as the time rate of linear momentum of a particle. It directly provides a measurable basis for the measurement of force in terms of mass and acceleration of a single particle. As such, the concept of linear momentum is not elaborated or emphasized for a single particle. However, we shall see in this module that linear momentum becomes a convenient tool to analyze motion of a system of particles - particularly with reference to internal forces acting inside the system.
It will soon emerge that Newton's second law of motion is more suited for the analysis of the motion of a particle like objects, whereas concept of linear momentum is more suited when we deal with the dynamics of a system of particles. Nevertheless, we must understand that these two approaches are interlinked and equivalent. Preference to a particular approach is basically a question of suitability to analysis situation.
Let us now recapitulate main points about linear momentum as described earlier :
(i) It is defined for a particle as a vector in terms of the product of mass and velocity.
P = mv
p = m v
The small "p" is used to denote linear momentum of a particle and capital "P" is used for linear momentum of the system of particles. Further, these symbols distinguish linear momentum from angular momentum (L) as applicable in the case of rotational motion. By convention, a simple reference to "momentum" means "linear momentum".
(ii) Since mass is a positive scalar quantity, the directions of linear momentum and velocity are same.
(iii) In physical sense, linear momentum is said to signify the "quantum or quantity of motion". It is so because a particle with higher momentum generates greater impact, when stopped.
(iv) The first differentiation of linear momentum with respect to time is equal to external force on the single particle.
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Momentum is a conserved quantity, meaning that the total momentum of any closed system (one not affected by external forces) cannot change. Although originally seen to be due to Newton's laws, this law is also true in special relativity, and with appropriate definitions a (generalized) momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity. I like to share this Linear Accelerator with you all through my article.
We have briefly defined linear momentum, while describing Newton's second law of motion. The law defines force as the time rate of linear momentum of a particle. It directly provides a measurable basis for the measurement of force in terms of mass and acceleration of a single particle. As such, the concept of linear momentum is not elaborated or emphasized for a single particle. However, we shall see in this module that linear momentum becomes a convenient tool to analyze motion of a system of particles - particularly with reference to internal forces acting inside the system.
It will soon emerge that Newton's second law of motion is more suited for the analysis of the motion of a particle like objects, whereas concept of linear momentum is more suited when we deal with the dynamics of a system of particles. Nevertheless, we must understand that these two approaches are interlinked and equivalent. Preference to a particular approach is basically a question of suitability to analysis situation.
Let us now recapitulate main points about linear momentum as described earlier :
(i) It is defined for a particle as a vector in terms of the product of mass and velocity.
P = mv
p = m v
The small "p" is used to denote linear momentum of a particle and capital "P" is used for linear momentum of the system of particles. Further, these symbols distinguish linear momentum from angular momentum (L) as applicable in the case of rotational motion. By convention, a simple reference to "momentum" means "linear momentum".
(ii) Since mass is a positive scalar quantity, the directions of linear momentum and velocity are same.
(iii) In physical sense, linear momentum is said to signify the "quantum or quantity of motion". It is so because a particle with higher momentum generates greater impact, when stopped.
(iv) The first differentiation of linear momentum with respect to time is equal to external force on the single particle.
Having problem with physics projects for class 12 cbse Read my upcoming post, i will try to help you.