Information AboutMomentum |
| CATEGORIES ABOUT MOMENTUM | |
| physical quantity | |
| mechanics | |
| introductory physics | |
| fundamental physics concepts | |
| conservation laws | |
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In Classical Mechanics momentum ( Pl. momenta; SI unit Kg M/s ) is the product of the Mass and Velocity of an object. For more accurate measures of momentum, see the section "modern definitions of momentum" on this page. In general the momentum of an object can be conceptually thought of as the tendency for an Object to continue to move in its direction of travel. As such, it is a natural consequence of Newtons First Law . Momentum is a Conserved quantity, meaning that the total momentum of any Closed System cannot be changed. MOMENTUM IN CLASSICAL MECHANICS 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. 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 symbol for momentum is usually denoted by a small p (bolded because it is a Vector ), so this can be written: : where p is the momentum, ''m'' is the mass, and '''v''' the velocity. The velocity of an object is given by its speed and its direction. Because momentum depends on velocity, it too has a Magnitude and a direction and is a Vector quantity. For example the momentum of a 5-kg bowling ball would have to be described by the statement that it was moving westward at 2 m/s. It is insufficient to say that the ball has 10 kg m/s of momentum because momentum is not fully described unless its direction is given. CONSERVATION OF MOMENTUM As far as we know, momentum is a conserved quantity. Conservation of momentum (sometimes also '''conservation of impulse''') states that the total amount of momentum of all the things in the universe will never change. One of the consequences of this is that the Center Of Mass of any System of Objects will always continue with the same velocity unless acted on by a force outside the system. Conservation of momentum is a consequence of the Homogeneity of space. In an isolated system (one where external forces are absent) the total momentum will be constant: this is implied by Newton's , which dictates that the forces acting between systems are equal in magnitude, but opposite in sign, is due to the conservation of momentum. Since momentum is a vector quantity it has direction. Thus when a gun is fired, although overall movement has increased compared to before the shot was fired, the momentum of the bullet in one direction is equal in magnitude, but opposite in sign, to the momentum of the gun in the other direction. These then sum to zero which is equal to the zero momentum that was present before either the gun or the bullet was moving. Conservation of momentum and collisions Momentum has the special property that, in a Closed System , it is always conserved, even in Collision s. Kinetic Energy , on the other hand, is not conserved in collisions if they are inelastic. Since momentum is conserved it can be used to calculate unknown velocities following a collision. A common problem in physics that requires the use of this fact is the collision of two particles. Since momentum is always conserved, the sum of the momentum before the collision must equal the sum of the momentum after the collision: :: :where the subscript ''i'' signifies initial, before the collision, and ''f'' signifies final, after the collision. Usually, we either only know the velocities before or after a collision and would like to also find out the opposite. Correctly solving this problem means you have to know what kind of collision took place. There are two basic kinds of collisions, both of which conserve momentum:
Elastic collisions A collision between two Pool or Snooker balls is a good example of an almost totally elastic collision. In addition to momentum being conserved when the two balls collide, the sum of kinetic energy before a collision must equal the sum of kinetic energy after: :: Since the 1/2 factor is common to all the terms, it can be taken out right away. =Head-on collision (1 dimensional) In the case of two objects colliding head on we find that the final velocity :: :: which can then easily be rearanged to =Multi dimensional collisions In any other case of objects colliding in more than one dimension the velocity is split into its axes with one axis going through the point of collision and the other axis/axes tangent to the point of collision. The velocity components that are tangent to the point of intersection remain the same, while the velocity through the point of collision is calculated the same as the one dimensional case. Inelastic collisions A common example of a perfectly inelastic collision is when two objects collide and then ''stick'' together afterwards. This equation describes the conservation of momentum: :: MODERN DEFINITIONS OF MOMENTUM Momentum in relativistic mechanics In relativistic mechanics momentum is defined as: u c
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