who changed Newton's second law into F=ma and why?

Question

physics

Answer 1

The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.

In an exact original 1792 translation (from Latin) Newton's Second Law of Motion reads:

LAW II: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. — If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

Newton here is basically saying that the rate of change in the momentum of an object is directly proportional to the amount of force exerted upon the object. He also states that the change in direction of momentum is determined by the angle from which the force is applied.

However, it must be remembered that for Newton, mass was constant and independent of velocity. To take "motion" (motu) as meaning momentum gives a false impression of what Newton believed. Since he took mass as constant (part of the constant of proportionality) it can, in modern notation, be taken to the left of the derivative as . If is dependent on velocity (and thus indirectly upon time) as we would now hold, then has to be included in the derivative, giving or .

Using momentum in the terminology (which would never have occurred to Newton) is a latter-day revision of the law to bring it into correspondence with special relativity.

Interestingly, Newton is restating in his further explanation another prior idea of Galileo, what we call today the Galilean transformation or the addition of velocities.

An interesting fact when studying Newton's Laws of Motion from the Principia is that Newton himself does not explicitly write formulae for his laws which was common in scientific writings of that time period. In fact, it is today commonly added when stating Newton's second law that Newton has said, "and inversely proportional to the mass of the object." This however is not found in Newton's second law as directly translated above. In fact, the idea of mass is not introduced until the third law.

In mathematical terms, the differential equation can be written as:


where is force, is mass, is velocity, is time and is the constant of proportionality. The product of the mass and velocity is the momentum of the object.

If mass of an object in question is known to be constant and using the definition of acceleration, this differential equation can be rewritten as:


where is the acceleration.

Using only SI Units for the definition of Newton, the constant of proportionality is unity (1). Hence:


However, it has been a common convention to describe Newton's second law in the mathematical formula where is Force, is acceleration and is mass. This is actually a combination of laws two and three of Newton expressed in a very useful form. This formula in this form did not even begin to be used until the 18th century, after Newton's death, but it is implicit in his laws.

Answer 2

the position'd you locate " in spite of the point of software of rigidity." it really is honestly incorrect. A = F/M applies if and on condition that F is pushed or pulled by the middle of mass/gravity. And, by definition, CM/G is the area re the body the position there's no torque even as a rigidity is utilized to it. otherwise, F will impose a torque and twisting action that isn't effect in linear acceleration besides the undeniable fact that that is going to effect in angular acceleration alpha = Fr/I the position Fr is torque over the radius of gyration r, and that i = kmr^2 is the prompt of inertia of the mass m. ok <= a million.00 reckoning on the shape and density distribution of the body. So do not get your knickers in a knot. you're really the finest option, it makes no experience, the irrespective area, because that is punctiliously incorrect. And now you recognize why.

Answer 3

It's just a simplification to teach physics in algebra form.

The actual law is F = dp/dt
(read as force equals the change in momentum over time)

dp/dt is a derivative of momentum (p=mass * velocity), which includes two terms:
m(dv/dt) and v(dm/dt)
[This is read as mass times the change in velocity over time, and velocity times the change in mass over time]

since most objects examined in a Physics 1 class do not change their mass over time, the second of those two terms is zero.
Example: A ball thrown through the air has the same mass the whole time, but a rocket that's burning it's onboard fuel has a changing mass.

The only term that's left is m(dv/dt), and dv/dt is the same as acceleration. (Change in velocity per time).

Therefore, F = ma [...for objects whose mass is constant]

Answer 4

That would be Newton. In Principia (its in Latin in case you want to read it). And he did it because a mathematical formulation is the only way to handle the universe quantitatively and predictively.