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:
“I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”
—Isaac Newton (1642–1727)
“The so-called law of induction cannot possibly be a law of logic, since it is obviously a proposition with a sense.—Nor, therefore, can it be an a priori law.”
—Ludwig Wittgenstein (1889–1951)
“He could jazz up the map-reading class by having a full-size color photograph of Betty Grable in a bathing suit, with a co- ordinate grid system laid over it. The instructor could point to different parts of her and say, “Give me the co-ordinates.”... The Major could see every unit in the Army using his idea.... Hot dog!”
—Norman Mailer (b. 1923)
“I found a dimpled spider, fat and white,
On a white heal-all, holding up a moth
Like a white piece of rigid satin cloth—
Assorted characters of death and blight”
—Robert Frost (1874–1963)
“When the landscape buckles and jerks around, when a dust column of debris rises from the collapse of a block of buildings on bodies that could have been your own, when the staves of history fall awry and the barrel of time bursts apart, some turn to prayer, some to poetry: words in the memory, a stained book carried close to the body, the notebook scribbled by hand—a center of gravity.”
—Adrienne Rich (b. 1929)