# Q & A: Newton’s Laws

Q:
Newton’s 4th law?! Why isn’t (inverse square law of) attraction between masses included as the 4th law of Newton, i.e.: 1) a = f/m 2) f = ma 3) Sum(force) on the interface = 0 4) f = GmM/r^2
- Mehran (age 53)
Lisle, Illinois
A:
Mehran-

That's a pretty strange list of Newton's laws you've got there.

Usually the first law is given as the law of inertia, i.e. if something has no forces acting on it then it keeps going at a steady speed in a straight line.

The second law is often given as F=ma or a= F/m, i.e. the acceleration is just determined by the force on the object divided by its mass. There would be no point in listing the same law twice in slightly different form. Of course you can think of the first law as a special case of the second, when F=0.

The third law is that the forces which two objects exert on each other are always the same size and pointing in exactly opposite directions. Since the force is just the rate of change of the momentum, this says that if you have a collection of objects exerting forces on each other, but not feeling any forces from the outside, then the total momentum of the collection doesn't change. This way of stating the law actually holds up best in modern physics.

There's no particular reason which we know of for leaving gravity off the list of Newton's force laws. Unlike the first two laws, and maybe the third, it actually is due to Newton and not his predecessors.

Newton also investigated a great variety of other phenomena. For example, he made great strides in our understanding of the spectrum of visible light. He also made tremendous advances in mathematics, inventing calculus along the way. Any short list of "Newton's Laws" leaves out a huge number of his contributions.

Mike W. (and Tom)

(published on 10/22/2007)