How can Newton's first law be a consequence of Newton's second law?

Question

Amelia Adams · Accepted Answer

Short answer: by considering #F=ma#
Long answer: the First Law doesn't really follow from the Second; well, at least it's not redundant

According to Newton's First Law of Motion, a body will remain at rest or travel at a constant speed unless it is affected by an outside force. Newton's Second Law of Motion states that the net force that acts upon a body is equal to the mass of the body multiplied by the acceleration due to the net force. In other words, #F_"net"=ma#. Now, one can argue that Newton's Second Law of Motion leads to the First Law. Consider this: since #F_"net"=ma#, with zero net force (no external forces), #0=ma#. Now, #m# is some finite positive value. In other words, this means that #a=0#. By definition, then, there is constant velocity (possibly constant zero velocity). Thus, it seems that Newton's Second Law of Motion leads to the First Law. #--------------------# Okay, let's examine the more thorough response now. Imagine the following situation: you are in orbit around the earth. We will take your perspective (or reference frame) into consideration. You have no velocity because you are motionless, but you are subject to the force of gravity because there is no other force to counteract it. This means that, according to Newton's Second Law, you must be accelerating in the direction of the earth. So why don't you fall to the ground? Newton's Second Law does not apply in a non-inertial reference frame because your perspective (reference frame) is accelerating in perspective to an inertial reference frame. This means that your perspective (reference frame) is a non-inertial reference frame. If the preceding two paragraphs are a little confusing to you, that's because they simply explain that there are some situations in which Newton's Second Law is not applicable. In order to address this, Newton had to define a "force" in a way that makes sense, which is how Newton's First Law came to be. Taking into consideration the First Law, which states that unless an external force acts upon a body, it will remain at rest or continue along its path at a constant velocity, you could argue that this law appropriately defines a force as something that moves a ball from rest or changes its velocity, preventing the Second Law from applying in the scenario described above. To put it another way, even though the First Law is required to define what a force is, the Second Law appears to incorporate it. Still, at least there isn't a duplication of the two laws.

Julia Aguilar · Answer

undefined Newton's first law states that an object will remain at rest or in uniform motion unless acted upon by an external force. This can be considered a consequence of Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. If there is no net force acting on an object (i.e., the sum of all forces is zero), according to Newton's second law, its acceleration will be zero. Therefore, the object will either remain at rest or continue to move with constant velocity, in accordance with Newton's first law.