Difference between revisions of "Newton's Laws of Motion"
| Line 14: | Line 14: | ||
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 p<sub>0</sub> on another, the first object's momentum will change by -p<sub>0</sub>. This can be viewed as a consequence of [[Noether's Theorem]]; the associated [[symmetry]] is that the laws of physics do not change | + | The third law states that momentum is always conserved. If one object imparts a momentum p<sub>0</sub> on another, the first object's momentum will change by -p<sub>0</sub>. 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). |
Revision as of 14:58, July 6, 2007
Isaac Newton's 3 laws of motion form the basis for classical mechanics. They are:
1) An object in motion will remain in motion unless acted upon by an outside force. An object at rest will remain at rest unless acted upon by an outside force.
2) The rate of change of an object's momentum is equal to the net force acting on it (<math>F = dp/dt </math>, sometimes written as <math>F = m*a</math>).
3) For every action there is an equal and opposite reaction; or, more precisely, the total momentum of any isolated system is always constant.
Explanation
The first law defines an inertial 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. 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 under spatial translations (that is, the laws of physics are the same everywhere).