“Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum
lineam rectam qua vis illa imprimitur. ”
This was translated quite closely in Motte’s 1729 translation as:
“Law II: The alteration of motion is ever proportional to the motive force impress’d; and is
made in the direction of the right line in which that force is impress’d.”
(Modern translation) second law: In an inertial reference frame, the vector sum of the forces
“F” on an object is equal to the mass “m” of that object multiplied by the acceleration “a” of
the object.
According to modern ideas of how Newton was using his terminology, this is
understood, in modern terms, as an equivalent of (Anon 2020):
The change of momentum of a body is proportional to the impulse impressed on the body
and happens along the straight line on which that impulse is impressed.
This may be expressed by the formula F ¼ p', where p' is the time derivative of
the momentum p. This equation can be seen clearly in the Wren Library of Trinity
College, Cambridge, in a glass case in which Newton’s manuscript is open to the
relevant page.
Motte’s 1729 translation of Newton’s Latin continued with Newton’s commentary on the second law of motion, reading:
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.
The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively
discussed by historians of science, along with the relations between Newton’s
formulation and modern formulations (Newton 1729).
2.1.2.1 Formulation of Newton’s Second Law
The second law states that the rate of change of momentum of a body is directly
proportional to the force applied, and this change in
dp
dt momentum takes place in the
direction of the applied force, F:
F ¼
dp
dt
¼
d mv
ð Þ
dt
The second law can also be stated in terms of an object’s acceleration. It is
important to note that we cannot derive a general expression for Newton’s second
law for variable mass systems by treating the mass in F ¼ dP/dt ¼ d(mv) as a
8
2 Stress and Strain in Continuum
lineam rectam qua vis illa imprimitur. ”
This was translated quite closely in Motte’s 1729 translation as:
“Law II: The alteration of motion is ever proportional to the motive force impress’d; and is
made in the direction of the right line in which that force is impress’d.”
(Modern translation) second law: In an inertial reference frame, the vector sum of the forces
“F” on an object is equal to the mass “m” of that object multiplied by the acceleration “a” of
the object.
According to modern ideas of how Newton was using his terminology, this is
understood, in modern terms, as an equivalent of (Anon 2020):
The change of momentum of a body is proportional to the impulse impressed on the body
and happens along the straight line on which that impulse is impressed.
This may be expressed by the formula F ¼ p', where p' is the time derivative of
the momentum p. This equation can be seen clearly in the Wren Library of Trinity
College, Cambridge, in a glass case in which Newton’s manuscript is open to the
relevant page.
Motte’s 1729 translation of Newton’s Latin continued with Newton’s commentary on the second law of motion, reading:
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.
The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively
discussed by historians of science, along with the relations between Newton’s
formulation and modern formulations (Newton 1729).
2.1.2.1 Formulation of Newton’s Second Law
The second law states that the rate of change of momentum of a body is directly
proportional to the force applied, and this change in
dp
dt momentum takes place in the
direction of the applied force, F:
F ¼
dp
dt
¼
d mv
ð Þ
dt
The second law can also be stated in terms of an object’s acceleration. It is
important to note that we cannot derive a general expression for Newton’s second
law for variable mass systems by treating the mass in F ¼ dP/dt ¼ d(mv) as a
8
2 Stress and Strain in Continuum