Newton's Second Law For A System of Rigid Bodies
To consider rigid body dynamics, Newton's second law must be extended to define the relationship between the movement of a rigid body and the system of forces and torques that act on it.
Newton's formulated his second law for a particle as, "The change of motion of an object is proportional to the force impressed and is made in the direction of the straight line in which the force is impressed." Because Newton generally referred to mass times velocity as the "motion" of a particle, the phrase "change of motion" refers to the mass times acceleration of the particle, and so this law is usually written as
where F is understood to be the only external force acting on the particle, m is the mass of the particle, and a is its acceleration vector. The extension of Newton's second law to rigid bodies is achieved by considering a rigid system of particles.
Read more about this topic: Rigid Body Dynamics
Famous quotes containing the words newton, law, system, rigid and/or bodies:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
“An endless imbroglio
Is law and the world,—
Then first shalt thou know,
That in the wild turmoil,
Horsed on the Proteus,
Thou ridest to power,
And to endurance.”
—Ralph Waldo Emerson (1803–1882)
“It is not easy to construct by mere scientific synthesis a foolproof system which will lead our children in a desired direction and avoid an undesirable one. Obviously, good can come only from a continuing interplay between that which we, as students, are gradually learning and that which we believe in, as people.”
—Erik H. Erikson (20th century)
“It’s fairly obvious that American education is a cultural flop. Americans are not a well-educated people culturally, and their vocational education often has to be learned all over again after they leave school and college. On the other hand, they have open quick minds and if their education has little sharp positive value, it has not the stultifying effects of a more rigid training.”
—Raymond Chandler (1888–1959)
“An impersonal and scientific knowledge of the structure of our bodies is the surest safeguard against prurient curiosity and lascivious gloating.”
—Marie Carmichael Stopes (1880–1958)