Newton's Laws of Motion - Newton's First Law

Newton's First Law

The first law law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Velocity is a vector quantity which expresses both the object's speed and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant.

The first law can be stated mathematically as

$\sum \mathbf{F} = 0\; \Rightarrow\; \frac{\mathrm{d} \mathbf{v} }{\mathrm{d}t} = 0.$

Consequently,

An object that is at rest will stay at rest unless an unbalanced force acts upon it.
An object that is in motion will not change its velocity unless an unbalanced force acts upon it. This is known as uniform motion.

An object continues to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest (demonstrated when a tablecloth is skillfully whipped from under dishes on a tabletop and the dishes remain in their initial state of rest). If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continually move in outer space. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely.

Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. The first law of motion postulates the existence of at least one frame of reference called a Newtonian or inertial reference frame, relative to which the motion of a particle not subject to forces is a straight line at a constant speed. Newton's first law is often referred to as the law of inertia. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero. In this sense, the first law can be restated as:

In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle initially at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it.

Newton's laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity.

Read more about this topic: Newton's Laws Of Motion

Famous quotes containing the words newton and/or law:

“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)

“Half the testimony in the Bobbitt case sounded like Sally Jesse Raphael. Juries watch programs like this and are ready to listen.”
—William Geimer, U.S. law educator. New York Times, p. B18 (January 28, 1994)