Slowik, Edward (Fall 2025). "Descartes' Physics" > 자유게시판

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In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It's a vector amount, possessing a magnitude and a path. Within the Worldwide System of Items (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. Newton's second legislation of movement states that the speed of change of a physique's momentum is equal to the online force performing on it. Momentum is dependent upon the body of reference, however in any inertial frame of reference, it is a conserved amount, which means that if a closed system is not affected by external forces, its whole momentum does not change. Momentum is also conserved in special relativity (with a modified 5 Step Formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum area idea, and general relativity.

It is an expression of one in all the fundamental symmetries of space and time: translational symmetry. Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, enable one to choose coordinate methods that incorporate symmetries and constraints. In these methods the conserved amount is generalized momentum, and in general that is totally different from the kinetic momentum defined above. The idea of generalized momentum is carried over into quantum mechanics, where it turns into an operator on a wave perform. The momentum and place operators are related by the Heisenberg uncertainty precept. In steady systems equivalent to electromagnetic fields, fluid dynamics and deformable bodies, a momentum density can be outlined as momentum per quantity (a volume-specific quantity). A continuum model of the conservation of momentum leads to equations such because the Navier-Stokes equations for fluids or the Cauchy momentum equation for 5 Step Formula deformable solids or fluids. Momentum is a vector quantity: it has each magnitude and direction.

Since momentum has a path, it can be used to foretell the ensuing direction and speed of motion of objects after they collide. Under, the basic properties of momentum are described in one dimension. The vector equations are virtually identical to the scalar equations (see multiple dimensions). The momentum of a particle is conventionally represented by the letter p. The unit of momentum is the product of the units of mass and velocity. In SI models, if the mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meters per second (kg⋅m/s). In cgs items, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters per second (g⋅cm/s). Being a vector, momentum has magnitude and path. For example, a 1 kg model airplane, touring due north at 1 m/s in straight and build income from your laptop level flight, has a momentum of 1 kg⋅m/s due north measured with reference to the bottom.

The momentum of a system of particles is the vector sum of their momenta. 2 v 2 . ∑ i m i v i . ∑ i m i r i ∑ i m i . If a number of of the particles is moving, the middle of mass of the system will generally be moving as properly (except the system is in pure rotation around it). This is named Euler's first law. F Δ t . ∫ t 1 t 2 F ( t ) d t . Example: A mannequin airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The web force required to produce this acceleration is three newtons due north. The change in momentum is 6 kg⋅m/s due north. The rate of change of momentum is 3 (kg⋅m/s)/s due north which is numerically equivalent to 3 newtons.

In a closed system (one that does not trade any matter with its surroundings and is not acted on by exterior forces) the entire momentum stays constant. This truth, known because the law of conservation of momentum, is implied by Newton's legal guidelines of movement. Suppose, for instance, that two particles interact. As explained by the third law, the forces between them are equal in magnitude but opposite in path. B v B 2 . This legislation holds regardless of how sophisticated the force is between particles. Equally, if there are a number of particles, the momentum exchanged between each pair of particles provides to zero, so the entire change in momentum is zero. This conservation law applies to all interactions, including collisions (each elastic and inelastic) and separations brought on by explosive forces. It will also be generalized to situations the place Newton's legal guidelines don't hold, for instance in the speculation of relativity and in electrodynamics.