Newton's second law is a law in the sense that when you are given the force $F$, given the mass $m$, you use the law to obtain $a=F/m$ and then solve the motion. To him, mass is just something measured by a balance. My high school teacher couldn't answer my questions very well. I was also confused by the meaning of mass, whether the second law is a law or a definition, etc. I remember I asked my high school teacher exactly the same question in the OP's post. I had a lot of questions similar to the OP's. I have to say I found Newton's laws very uneasy to understand when I was in high school. They all have a purpose, they all do something. In summary: the third law constrains the forces to consider, the second makes predictions so you can test the force laws, and the first constrains the (too many?) solutions that the second law allows. And in fact it sometimes forces the jerk to be discontinuous. So Newton's first law has content, it excludes those motions. A body can experience no force at an instant (and hence no acceleration) and have no velocity at that instant and yet start moving again (if it had a continuous and nonzero jerk at that instant it would have to). It is exactly as big an error (to just assume that without a law or principle). To jump from a zero acceleration to the velocity staying constant forever after is to simply ignore the possibility of a nonzero jerk. The student ignored the possibility of a nonzero acceleration. Jumping from a pointwise zero acceleration to a constant velocity is just like a student analyzing projectile motion, noting that the velocity is zero at the top and then assuming the projectile stays there forever (student thinks once the velocity is zero for an instant, that therefore the position stays constant forever after). The second law does tell us that F=0 implies a=0, but that does not mean that the velocity is constant, merely that the acceleration is zero, but if you have a nonzero jerk, then the acceleration can change. Since you said F=0 implied a=0, let me point out that yes that is true, but Newton's first law says more than a=0 it says that it stays at rest if at rest and has the same constant motion if in constant motion. So adding the first law says to throw out those solutions. 61, 58 (1993) ) to have solutions to F=ma that violate Newton's first law. I'm not saying that historically Newton knew this, but it is possible (see Nonuniqueness in the solutions of Newton’s equation of motion by Abhishek Dhar Am. Newton's first law then excludes certain solutions that the second law allowed. This works because he postulates that we can test force laws by using calculus and then looking at the prediction from solutions to second order differential equations. Newton's second law turns these force laws into predictions about motion, thus allowing the force laws to be tested, not just eliminated for violating conservation of momentum. Newton's third law constrains what force laws you consider (effectively you only use/consider force laws that conserve momentum). Newton's first law is necessary, because it does something. Similarly if we take the second law as the definition of an inertial frame, it should not be necessary to know whether the frame is inertial or not to apply the second law (to check that the frame is inertial). Because we take the first law as definition of an inertial reference frame. We don't need to know it in advance about the frame of reference to apply the first law. Thus unless we know in advance that a frame is inertial, we can't apply the second law.īut then why this is not the problem for the first law? One can say (can one?) we cannot apply the second law to define a reference frame because it is only applicable to inertial frames. Now if we put $F=0$ we get $a=0$ which is Newton's first law.īefore asking I did some searching and I got this: Newtons first law is necessary to define inertial reference frame on which the second law can be applied.īut why can't we just use Newton's second law to define an inertial frame? So if $F=0$ but $a$ is not equal to 0 (or vice versa), the frame is non-inertial.
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