Now, we rely on three almost self-evident definitions and investigate one of the most important achievements of human beings in the field of natural science: The Newton’s laws of motion.
- The first definition, the “amount of matter” or “mass”, is the product of the density and volume of an object. As we know, if the density of an object doubles, the amount of matter in the same measured space is doubled and the amount of matter in the space twice or triple, is four or six times.
(Mass) = (Density) multiplied by (Volume)
- The second definition, the “momentum”, is the product of the velocity and mass of an object. Motion of an object is actually the sum of the motions of all its constituent parts. Consequently, if the mass doubles at constant velocity, the momentum is doubled and if the velocity doubles, the momentum will be quadrupled.
(Momentum) = (Velocity) multiplied by (Mass)
- Third, “inertial frame of reference” is a frame of reference, consist of an abstract coordinate system, in which bodies, whose net force acting upon them is zero, are not accelerated. A rotating frame of reference is also accelerated.
Now we investigate Newton’s laws:
- The first law states that in an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
So, we know that if an object is moving at a constant velocity and in a straight-line, its momentum will remain steady. This phenomenon is due to the innate force of matter, called “inertia”.
- The second law states that in an inertial frame of reference, the change in the momentum is proportional to the amount of forces involved and the direction of the net force.
Therefore, if a force changes the momentum of an object, doubling the force will double the motion and tripling the force will triple the motion.
- The third law states that for every action there always is an equal reaction, but in the opposite direction.
Therefore, if two objects are applying force on each other, change in the momentum in each is proportional to the equal forces applied on, and the inverse of the mass of each object.
Also, with a closer look at Newton’s laws, one can infer the following concepts:
The first law expresses the concept of no net force. Without a definition of no net force, it wouldn’t be possible to understand the concept of force.
The second law indicates the proportion between force and time derivative of the momentum. If the mass of an object remains constant, any change in the velocity is the result of applying not balanced forces.
(Force) = (Mass (fixed)) multiplied by (Time derivative of velocity (Acceleration))
We also demonstrated that one can deduce the practical definition of mass from the third law. In an isolated and ideal system consisting of two masses, we have:
(Mass of the second object) = (Mass of the first object (unit mass)) multiplied by (Time derivative of velocity of the first object) divided by (Time derivative of velocity of the second object)
Newton’s laws are an unrivaled example of exploration based on physical observation. Today, it’s obvious that if we are placed in a chamber like a spacecraft which has a variable velocity (acceleration), we can sense the force, or even its magnitude, without having to rely on an external reference.
Although recent discoveries in electromagnetism and Einstein’s theory of relativity have demonstrated that within the boundaries of certain observations of the physics world, there are discrepancies from the Newton’s laws; but, apart from these specific boundaries of observation, Newton’s laws are always accurately true.
Here we described Newton’s laws only as an example of physical observation and discovery. In general, physical laws are theoretical principles that are derived from certain facts and are defined for a particular category or group of phenomena. While a theory is a well-substantiated explanation of nature that is compatible with the scientific method and is confirmed through observation.