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:
“Glorious things of thee are spoken, Zion city of our God!
He, whose word cannot be broken, Form’d for thee his own abode:
On the rock of ages founded, What can shake thy sure repose?
With salvation’s walls surrounded Thou may’st smile at all thy foes.”
—John Newton (1725–1807)
“The law will never make a man free; it is men who have got to make the law free.”
—Henry David Thoreau (1817–1862)
“Fear, coercion, punishment, are the masculine remedies for moral weakness, but statistics show their failure for centuries. Why not change the system and try the education of the moral and intellectual faculties, cheerful surroundings, inspiring influences? Everything in our present system tends to lower the physical vitality, the self-respect, the moral tone, and to harden instead of reforming the criminal.”
—Elizabeth Cady Stanton (1815–1902)
“Let’s call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don’t require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.”
—Saul Kripke (b. 1940)
“The repossession by women of our bodies will bring far more essential change to human society than the seizing of the means of production by workers.”
—Adrienne Rich (b. 1929)