# Newton laws of mechanics

The three basic laws describing the motion of material bodies under the action of forces applied to them.

First law: If no forces act on a material point (or if the forces applied to it are in equilibrium), then relative to an inertial reference system the material point is in a state of rest or uniform rectilinear motion.

Second law: If a force $\mathbf F$ acts on a material point, then relative to an inertial reference system the point undergoes an acceleration $\mathbf a$ such that its product with the mass $m$ of the point is equal to $\mathbf F$:

$$m\mathbf a=\mathbf F.$$

Third law: Two material points act on each other with forces that are equal in absolute value but opposite in direction along the line joining the two points.

Newton's laws of mechanics cease to be valid for motions of objects of very small dimension (elementary particles) and for motions with velocities close to that of light.

The laws were stated by I. Newton in 1687.

#### Comments

#### References

[a1] | R.B. Lindsay, H. Margenau, "Foundations of physics" , Dover, reprint (1957) |

[a2] | D.E. Rutherford, "Classical mechanics" , Oliver & Boyd (1957) |

[a3] | Th.T. Taylor, "Mechanics: classical and quantum" , Pergamon (1976) |

**How to Cite This Entry:**

Newton laws of mechanics.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Newton_laws_of_mechanics&oldid=33734