FHSST Physics/Momentum

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The Free High School Science Texts: A Textbook for High School Students Studying Physics.
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Momentum
Definition - Momentum of a System - Change in Momentum - Properties - Impulse - Important Quantities, Equations, and Concepts


Momentum is the product of the mass and velocity of an object. In general the momentum of an object can be conceptually thought of as the tendency for an object to continue in its current state of motion, speed and direction.

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[edit]

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:

\mathbf{p}= m \mathbf{v}
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[edit]

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 first law of motion. Newton's third law of motion, the law of reciprocal actions, 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.