Newton's second law is so intuitively obvious

[bhobba]

This is most interesting. In his original preface to the first Russian edition (1940, sans Lifshitz) he clearly delineated theoretical physics from mathematical physics. His book is on theoretical physics :)

Interesting - just checked my well worn third edition and its not there.

Maybe I am more of a theoretical physicist - I don't know - my undergrad degree was in applied math and it just gelled so beautifully with that in my mind. At the root of a lot of math is symmetry - that physics was the same hit me like a thunderbolt.

Thanks
Bill

 

[harrylin]

Granted, "derived all of classical mechanics" is an overstatement, to put it mildly. There is much in classical mechanics that he did not touch upon at all, including such venerable subjects as statics.

As far as Hooke's law is concerned, he actually derived it, without using the name, in the section on small oscillations, where he showed that any potential energy at small deviations from equilibrium is approximated by $\frac k 2 (q - q_0)^2$. Note he actually derived it, not postulated as is done in some other texts.

Oh that's neat indeed!

 

[Andrew Mason]

Okay, that's a nice argument, but it implicitly makes the assumption that a force has the same magnitude in all frames of reference. How is that justified?

It is the same constant force that is seen to be constant in all frames. The force is constant because there is no change in the thing supplying the force. For example, a spring that is kept stretched to a constant distance; a very heavy weight that drops very slowly and supplies a force through a gear mechanism.

AM

 

[stevendaryl]

It is the same constant force that is seen to be constant in all frames. The force is constant because there is no change in the thing supplying the force. For example, a spring that is kept stretched to a constant distance; a very heavy weight that drops very slowly and supplies a force through a gear mechanism.

AM

But in Special Relativity, a force doesn't have the same magnitude in every reference frame. So to assume that it has the same magnitude in every reference frame is not an immediate consequence of the equivalence of all reference frames.

 

[Andrew Mason]

But in Special Relativity, a force doesn't have the same magnitude in every reference frame. So to assume that it has the same magnitude in every reference frame is not an immediate consequence of the equivalence of all reference frames.

But Galilean relativity does not apply in SR where time and space are not absolute. Those are premises in Galilean relativity.

In Galilean relativity all measurements of the thing supplying the force are identical in all IFRs while in SR they are not. For example, in Galilean relativity a spring stretched a certain distance as measured in one IFR is stretched the same distance in all IFRs. Not so in special relativity.

AM