Changes
tidy up formulae
The first law defines an [[inertia]]l [[frame of reference]] as one which is acted upon by no outside forces. In general, inertial frames are far easier to understand conceptually and deal with mathematically than accelerated frames.
The second law relates force and [[momentum]]. MathematicallyIn classical mechanics, momentum is <math>m \vec{v}</math> so, <math> \vec F = d\frac{d \vec {p}/}{dt } = \frac{d(m\ \vec v)/}{dt } = m\ \frac{d{\vec v}/}{dt } + \vec v\ \frac{dm/}{dt} = m\ \vec{a} + \vec v\ \frac{dm}{dt}</math>. Usually <math>dm/dt=0m</math>is constant, so the law is simplified to <math> \vec F = m\ d{\vec v}/dt = m\ \vec a</math>, or [[mass (science)|mass]] times [[acceleration]]. A notable exception is [[rocket]] motion, where <math>dm/dtm</math> is not 0constant, and so <math> \vec F = m\ \vec a</math> does not apply. Note that the quantities '''<math>\vec{F'''}</math>, '''<math>\vec{p'''}</math>, '''<math>\vec{v'''}</math>, and '''<math>\vec{a''' }</math> are all [[vector]] quantities—that is, they have an associated direction as well as a magnitude.
In general, the second law gives a way to predict the motion of an object by summing all the forces acting on that object.
The third law states that momentum is always conserved. If one object imparts a momentum p<submath>0\vec{p}_0</submath> on another, the first object's momentum will change by −p<submath>0\vec{p}_0</submath>. This can be viewed as a consequence of [[Noether's Theorem]]; the associated [[symmetry]] is that the laws of physics do not change under spatial translations (that is, the laws of physics are the same everywhere).
[[Category:Physics]]
[[Category:Mechanics]]
