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Momentum Brittany Vincent History of the concept • Mōmentum was not merely the motion, which was mōtus, but was the power residing in a moving object, captured by today's mathematical definitions. A mōtus, "movement", was a stage in any sort of change, while velocitas, "swiftness", captured only speed. The concept of momentum in classical mechanics was originated by a number of great thinkers and experimentalists. The first of these was Ibn Sina (Avicenna) circa 1000, during the Islamic Renaissance who referred to impetus as proportional to weight times velocity. René Descartes later referred to momentum as mass times velocity and as the fundamental force of motion. This allowed Descartes to maintain that mass and velocity are fundamental and conserved, everywhere and all the time. • The question has been much debated as to what Isaac Newton contributed to the concept. The answer is apparently nothing, except to state more fully and with better mathematics what was already known. Yet for scientists, this was the death knell for Aristotelian physics and supported other progressive scientific theories (i.e., Kepler's laws of planetary motion). Conceptually, the first and second of Newton's Laws of Motion had already been stated by John Wallis in his 1670 work, the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result. Wallis uses momentum and vis for force. Linear momentum of a particle • If an object is moving in any reference frame, then it has momentum in that frame. It is important to note that momentum is frame dependent. That is, the same object may have a certain momentum in one frame of reference, but a different amount in another frame. For example, a moving object has momentum in a reference frame fixed to a spot on the ground, while at the same time having 0 momentum in a reference frame attached to the object's center of mass. • The amount of momentum that an object has depends on two physical quantities: the mass and the velocity of the moving object in the frame of reference. In physics, the usual symbol for momentum is a bold p (bold because it is a vector); so this can be written – • where p is the momentum, m is the mass and v is the velocity. • Example: a model airplane of 1 kg traveling due north at 1 m/s in straight and level flight has a momentum of 1 kg m/s due north measured from the ground. To the dummy pilot in the cockpit it has a velocity and momentum of zero. • According to Newton's second law, the rate of change of the momentum of a particle is proportional to the resultant force acting on the particle and is in the direction of that force. The derivation of force from momentum is given below, however because mass is constant the second term of the derivative is 0 so it is ignored. • • or just simply – • where F is understood to be the resultant. • Example: a model airplane of 1 kg accelerates from rest to a velocity of 1 m/s due north in 1 s. The thrust required to produce this acceleration is 1 newton. The change in momentum is 1 kg m/s. To the dummy pilot in the cockpit there is no change of momentum. Its pressing backward in the seat is a reaction to the unbalanced thrust, shortly to be balanced by the drag. Linear momentum of a system of particles Relating to mass and velocity The linear momentum of a system of particles is the vector sum of the momenta of all the individual objects in the system: where P is the total momentum of the particle system, mi and vi are the mass and the velocity vector of the i-th object, and n is the number of objects in the system.It can be shown that, in the center of mass frame the momentum of a system is zero. Additionally, the momentum in a frame of reference that is moving at a velocity vcm with respect to that frame is simply: where: This is known as Euler's first law. Relating to force - General equations of motion The linear momentum of a system of particles can also be defined as the product of the total mass of the system times the velocity of the center of mass. This is commonly known as Newton's second law. For a more general derivation using tensors, we consider a moving body. assumed as a continuum, occupying a volume at a time, having a surface area, with defined traction or surface forces acting on every point of the body surface, body forces per unit of volume on every point within the volume, and a velocity field prescribed throughout the body. Following the previous equation, The linear momentum of the system is: By definition the stress vector is then Motion of a material body Links • http://en.wikipedia.org/wiki/Momentum • http://images.google.com/imgres?imgurl=http://webpage s.uah.edu/~wilderd/momentum.jpg&imgrefurl=http://web pages.uah.edu/~wilderd/resources.html&usg=__H5tv28u wZTdU6i44waoUJ7v1dPI=&h=545&w=600&sz=75&hl=e n&start=5&um=1&itbs=1&tbnid=- S_WjwpluSOd5M:&tbnh=123&tbnw=135&prev=/images %3Fq%3Dmomentum%26hl%3Den%26safe%3Dactive %26rls%3Dcom.microsoft:en-us:IE- Address%26rlz%3D1I7ADBS_en%26sa%3DN%26um% 3D1

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posted: | 8/21/2012 |

language: | English |

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