 | Newton's laws of motion: Encyclopedia II - Newton's laws of motion - Newton's second law
Newton's laws of motion - Newton's second law
Lex II: Mutationem motus proportionalem esse vi motrici impressae et fieri secundum lineam rectam qua vis illa imprimitur.
- The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction.
Newton's second law as originally stated in terms of momentum is
'An applied force is equal to the rate of change of momentum'.
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The physical meaning of this equation is that objects interact by exchanging momentum, and they do this via a force.
When the mass of the object is constant, the relation gives another useful form of the second law:
where is the acceleration of the object (i.e., the rate of change of its velocity ).
For example, if a bowstring exerts a constant force of 100 newtons on an arrow having a mass of 0.10 kg, then the arrow's acceleration will be 1000 m/s2 until it leaves the bow (after which the arrow will stop speeding up).
In these equations, is the net force, i.e., the sum of all the forces acting on the object. When the forces on the object all act along the same line, they can be added as positive and negative numbers, depending on their direction. When they do not all act along the same line, the total must be found by vector addition.
The quantity m, or mass, is a characteristic of the object. The greater the total force acting on an object, the greater the change in its acceleration will be. This equation, therefore, indirectly defines the concept of mass. In the equation, F = ma, a is directly measurable but F is not. The second law only has meaning if we are able to assert, in advance, the value of F. Rules for calculating force include Newton's law of universal gravitation, Coulomb's law, and other principles.
The statement in terms of momentum is also valid in special relativity if we express the momentum as , where γ is .
Other related archives1687, Coulomb's law, Galilean relativity, Galileo's Principle, Galileo's discovery, General Relativity, Inertia, Isaac Newton, Kepler's laws of planetary motion, Mercury, orbit of, Philosophiae Naturalis Principia Mathematica, Scientific laws named after people, acceleration, angular momentum, conservation, energy, force, forces, friction, inertial reference frames, law of universal gravitation, mass, momentum, net force, quantum mechanics, reference frames, relativity, special relativity, stars, sum, universe, vector, velocity
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