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:
“Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of thought, alone.”
—William Wordsworth (1770–1850)
“We ourselves are Jews by birth and not Gentile sinners; yet we know that a person is justified not by the works of the law but through faith in Jesus Christ. And we have come to believe in Christ Jesus, so that we might be justified by faith in Christ, and not by doing the works of the law, because no one will be justified by the works of the law.”
—Bible: New Testament, Galatians 2:15-16.
“Social and scientific progress are assured, sir, once our great system of postpossession payments is in operation, not the installment plan, no sir, but a system of small postpossession payments that clinch the investment. No possible rational human wish unfulfilled. A man with a salary of fifty dollars a week can start payments on a Rolls-Royce, the Waldorf-Astoria, or a troupe of trained seals if he so desires.”
—John Dos Passos (1896–1970)
“Pain hardens, and great pain hardens greatly, whatever the comforters say, and suffering does not ennoble, though it may occasionally lend a certain rigid dignity of manner to the suffering frame.”
—A.S. (Antonia Susan)
“People stress the violence. That’s the smallest part of it. Football is brutal only from a distance. In the middle of it there’s a calm, a tranquility. The players accept pain. There’s a sense of order even at the end of a running play with bodies stewn everywhere. When the systems interlock, there’s a satisfaction to the game that can’t be duplicated. There’s a harmony.”
—Don Delillo (b. 1926)