Newton's Laws of Motion wrote:Newton's First Law: Law of InertiaThis law is also called the Law of Inertia or Galileo's Principle.
Alternative formulations:
* Every body's center of mass continues in its state of rest, or of uniform motion in a right [straight] line, unless it is compelled to change that state by forces impressed upon it.
* An object in motion, will remain in motion and an object at rest, will remain at rest, unless acted upon by an unbalanced force (in which the NET force is not 0).
* A body's center of mass remains at rest, or moves in a straight line (at a constant velocity, v), unless acted upon by a net outside force.
In calculus notation, this may be expressed as:
Despite the fact that Newton's First Law appears to be a special case of Newton's Second Law, the First Law defines the reference frames in which the other two laws are valid. These reference frames are called inertial reference frames or Galilean reference frames, and are moving at constant velocity, that is to say, without acceleration. (Note that an object may have a constant speed and yet have a non-zero acceleration, as in the case of uniform circular motion. This means that the surface of the Earth is not an inertial reference frame, since the Earth is rotating on its axis and orbits around the Sun. However, for many experiments, the Earth's surface can safely be assumed to be inertial. The error introduced by the acceleration of the Earth's surface is minute.)
In less formal terms, Aristotle thought that things stood still if you left them alone, that to be at rest was natural, and that movement needed a cause. It would be natural to think thus, as any movement (except for that of celestial objects, which were deemed perfect) that one observes eventually stops because of friction. But Galileo's experiments, with a ball rolling down an inclined plane, found that "Things travel naturally at a steady speed (which may or may not be zero), if left alone".
Moving from Aristotle's "A body's natural state is at rest" to Galileo's discovery (Newton's First Law) was one of the most profound and important discoveries in physics. In everyday life, the force of friction usually acts upon moving objects, slowing them down and eventually bringing them to rest. Newton described a mathematical model from which one could derive the motions of bodies from elementary causes: forces.
Newton's Second Law: Fundamental law of dynamicsAlternative formulations:
* The rate of change in momentum is proportional to the net force acting on the object and takes place in the direction of the force.
* The acceleration of an object of constant mass is proportional to the resultant force acting upon it.
These formulations may be expressed mathematically in the following ways:
or
if m is constant.
where
* F is the force acting,
* m is the mass of the object in question,
* a is the object's acceleration,
* v is the object's velocity, and
* p = m\mathbf{v} collectively is called the object's momentum.
This equation expresses that
* the more net force acts on an object, the greater the change in its momentum will be.
The quantity m, or mass, in the above equation is a characteristic of the object. For an object of constant mass m (a constant of proportionality) the more net force acts 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.
But F = ma is not always valid. In general both the mass of the object and its velocity can be variable. For this case:
This equation works in cases when the mass is variable. This equation is also valid in special relativity if we express the momentum as
, where γ is
.
The physical meaning behind this equation is important as it implies that objects interact by exchanging momentum, and they do this via a force.
Taken together with Newton's Third Law of Motion, Newton's Second Law implies the Law of Conservation of Momentum.
Newton's Third Law: Law of reciprocal actionsAlternative formulations:
* Whenever one body exerts force upon a second body, the second body exerts an equal and opposite force upon the first body.
* Momentum is conserved.
The very common formulation "for every action there is an equal and opposite reaction" should be avoided, as it is, at best, ambiguous and confusing. A better formulation would be that when there exists a force acting on a body A, due to another body B, there exists also a reciprocal force, acting on body B, due to the existence of body A.
These formulations imply that if you strike an object with a force of 200 N, then the object also strikes you (with a force of 200 N). Not only do planets accelerate toward stars; but, stars accelerate toward planets. The reaction force has the opposite direction of action, and is of the same type and magnitude as the original force. However, it doesn't necessarily "line up" in space with the action. One example of this is a force on an electric dipole due to a point charge, when the dipole points in a direction perpendicular to the line connecting the point charge and the dipole. The force on the dipole due to the point charge is perpendicular to the line connecting them, so there is a reaction force on the point charge in the opposite direction, but these two force vectors are parallel and, even when extended to a line, they never cross each other in space.
It is often contended that Newton's third law is incorrect when electromagnetic forces are included: if a body A exerts a force on body B, then body B will in general exert a different force on body A (the force considered is the Lorentz force, generated by electric and magnetic fields). However, modern theory predicts that the electromagnetic field generated by such interactions itself transports momentum via electromagnetic radiation, and Newton's third law is valid if the momentum of the field is included in the calculations.
is Planck's constant (h) divided by 2π. (In some treatments, the "uncertainty" of a variable is taken to be the smallest width of a range which contains 50% of the values, which, in the case of normally distributed variables, leads to a larger lower bound of h/2π for the product of the uncertainties.) Note that this inequality allows for several possibilities: the state could be such that x can be measured with high precision, but then p will only approximately be known, or conversely p could be sharply defined while x cannot be precisely determined. In yet other states, both x and p can be measured with "reasonable" (but not arbitrarily high) precision.
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