what is a simple and short definition of newton's 2nd law of motion?

Answer 1

Newton's Fisrt Law says a body at rest tends to stay at rest. A body in motion tends to stay in motion in a straight line umless acted upon by some external force.

This means that if a body is changing its state of inertia then there is a force acting upon it.

A force needs to be applied to get it into motion if its at rest or if it is moving at a constant velovity in a straight line then for that state to change it must have a force applied as well.

So planets moving in curved paths must have a force applied (and of course that force is the gravitational attraction of another body ... the sun)

Newton's second law: historical development

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

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 mdv/dt. If m is dependent on velocity (and thus indirectly upon time) as we would now hold, then m has to be included in the derivative, giving dmv/dt or dp/dt

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:

F = k d(mv)/dt

where F is force, m is mass, v is velocity, t is time and k 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:

F = kma

where a is the acceleration.

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

F = ma

However, it has been a common convention to describe Newton's second law in the mathematical formula F = ma where F is Force, a is acceleration and m 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.

The second law states that the acceleration of an object is dependent upon two variables – the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.

The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors, in this law the direction of the force vector is the same as the direction of the acceleration vector.

Answer 2

Second Law Of Motion Definition

Answer 3

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RE:
what is a simple and short definition of newton's 2nd law of motion?

Answer 4

Definition Of Newton

Answer 5

Law 1: Inertia
Law 2: F=ma
Law 3: Equal and opposite forces

Answer 6

Those definitions were for the FIRST law, that of inertia.

The second law says F=ma, which means that the force that something can exert is directly proportional to the object's mass times it's acceleration.

Answer 7

Whatever is in motion will continue to be in motion unless acted upon by an opposing force. Or is that the 1st law?

Answer 8

There are many people who would make fun of the prospect of changing their fates. This is due to the fact that it believes that nobody gets more that exactly what is written in his destiny.

Answer 9

force is inversely proportional to the mass of the object times gravitational acceleration