Why do some people say that Newton's Second law is the real Law of Motion?

[Dadface]

I looked at the Nortons dome video and got stuck pretty early on (just after one minute and thirty seconds).The presenter gave a key equation that describes the dome but the equation does not balance in terms of units.Is the whole analysis invalidated or have I overlooked something?

 

[netgypsy]

AXIOMATA, SIVE LEGES MOTUS

[Leges solæ descripta sunt, commentariis prætermissis.]

Lex I

Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.

Lex II

Mutationem motus proportionalem esse vi motrici impressæ, & fieri secundum lineam rectam qua vis illa imprimitur.

Lex III

Actioni contrariam semper & æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales & in partes contrarias dirigi.

 

[netgypsy]

Pretty straight forward. You think Isaac is chuckling at this conversation?

 

[Fredrik]

I looked at the Nortons dome video and got stuck pretty early on (just after one minute and thirty seconds).The presenter gave a key equation that describes the dome but the equation does not balance in terms of units.Is the whole analysis invalidated or have I overlooked something?

I hope so, because otherwise no curved shapes can be described mathematically. Probably best to think of everything as dimensionless. Alternatively, you can imagine that there's a (dimensionless 1)*(appropriate unit) multiplying every term.

 

[Rakinniya]

 

[netgypsy]

I found this one for first level physics class. The essential point being that before and after the interaction the velocities of the masses (two in this case) are constant so the derivative of the velocity times the constant mass is zero. From this the F one = -F two is then concluded.

Let the net momentum of a system of two bodies of mass m1 and m2 be p where p=p1+p2.from the second law net external force on the body =dp1/dt+dp2/dt. if the total momentum in any direction is constant then dp1/dt+dp2/dt=0(derivative of a constant is zero.)let the velocities of the bodies change from u1 to v1 and u2 to v2 in time t due to their mutual interaction. then m1(v1-u1)/t+m2(v2-u2)/t=0 (since dp/dt is time rate of change of momentum.) again we know (v-u)/t=acceleration. so m1f1+m2f2=0. again from the second law we get force =mass*acceleration. so f1+f2=0 and so f1= -f2. which shows thr force applied by the first body on the second is equal in magnitude but opposite in direction to the force applied by the second on the first. this is stated in the third law.thus it is derieved from the second law.