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)
“A crime persevered in a thousand centuries ceases to be a crime, and becomes a virtue. This is the law of custom, and custom supersedes all other forms of law.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“For the universe has three children, born at one time, which reappear, under different names, in every system of thought, whether they be called cause, operation, and effect; or, more poetically, Jove, Pluto, Neptune; or, theologically, the Father, the Spirit, and the Son; but which we will call here, the Knower, the Doer, and the Sayer. These stand respectively for the love of truth, for the love of good, and for the love of beauty.”
—Ralph Waldo Emerson (1803–1882)
“During our twenties...we act toward the new adulthood the way sociologists tell us new waves of immigrants acted on becoming Americans: we adopt the host culture’s values in an exaggerated and rigid fashion until we can rethink them and make them our own. Our idea of what adults are and what we’re supposed to be is composed of outdated childhood concepts brought forward.”
—Roger Gould (20th century)
“The yellow pool has overflowed high up on Clooth-na-Bare,
For the wet winds are blowing out of the clinging air;
Like heavy flooded waters our bodies and our blood;
But purer than a tall candle before the Holy Rood
Is Cathleen, the daughter of Houlihan.”
—William Butler Yeats (1865–1939)