Changes

The second law relates force and [[momentum]].  Mathematically, <math>F = dp/dt = d(m*v)/dt = m*dv/dt + v*dm/dt</math>.  Usually <math>dm/dt=0</math>, so the law is simplified to <math>F = m*dv/dt = m*a</math>, or mass times acceleration.  A notable exception is [[rocket]] motion, where <math>dm/dt</math> is not 0, and so <math>F = m*a</math> does not apply.  Note that the quantities '''F''', '''p''', '''v''', and '''a''' 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 second law relates force and [[momentum]].  Mathematically, <math>F = dp/dt = d(m*v)/dt = m*dv/dt + v*dm/dt</math>.  Usually <math>dm/dt=0</math>, so the law is simplified to <math>F = m*dv/dt = m*a</math>, or mass times acceleration.  A notable exception is [[rocket]] motion, where <math>dm/dt</math> is not 0, and so <math>F = m*a</math> does not apply.  Note that the quantities '''F''', '''p''', '''v''', and '''a''' 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 p₀ on another, the first object's momentum will change by -p₀.  This can be viewed as a consequence of [[Noether's Theorem]]; the associated [[symmetry]] is that the laws of physics do not change over small time periods.

The third law states that momentum is always conserved.  If one object imparts a momentum p₀ on another, the first object's momentum will change by -p₀.  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).