Newton's First and Second Law the Same
Date: Fall 2012
Is Newton's First Law just a special case of Newton's Second Law of Motion? Is the First Law is necessary if it is a special case of Second Law?
Just to lay out the problem you seek an answer to: The first law, a force is needed to change position or motion. The second law is that the force is of proportion to mass and acceleration. Is the former needed?
The first law names force, defined as something that changes a body having inertia. The second law defines the boundaries and properties of the force.
Without the first law, the second defines a force to do... What?
Issac Newton was a very insightful, meticulous person. He got it right by defining first, the problem and variables; then second, the properties of those variables with more variables. His insight and approach of building variables and definitions has been of great utility for many years. We define the problem first, then set about locating variables and defining them as we work through and solve.
For myself, both are needed. Thanks! Peter E. Hughes, Ph.D. Milford, NH
You are correct, Newton’s First Law is a special case of the Second Law. So in that sense it is not really “necessary.” But in another sense, it makes sense to give it independent attention. The First Law could be true even if the Second Law were not true, but the second law could not be true if the First Law were not. Basically, the first law defines “external net force” as any influence causing an object to accelerate, and the Second Law specifies how a particular force will influence a mass.
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
Newton's First Law just sets the principle that an object of a given mass stays in uniform motion (constant speed and direction) if no external forces are applied to it.
Newton's Second Law simply defines the relationships between mass, force and acceleration.
F = ma = m (dv/dt)
The two laws are related in that if no force is applied (F=0), the body of mass is in uniform motion at a constant speed and direction (velocity), meaning acceleration a=0. First Law.
If a force, F, is applied, the body of mass will change velocity with time (dv/dt) or in other words, will accelerate. Second Law.
Hope that helps.
On the contrary, All three are quite necessary.
The second is based upon the first. The first law tells that motion requires a force, otherwise things stand still.
The second defines and quantifies force in a measurable manner by relating it to acceleration and mass.
Hope this helps.
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Update: November 2011