Tuesday, June 21, 2005

Basic Phylosophy of The Classic Mechanics

Dynamics (mechanics)

In mathematics and physics, dynamics is the branch of mechanics that is concerned with the effects of forcess on the motion of objects.

Force

Force isn't really a fundamental quantity in physics, despite the inertia of physics education still introducing students to physics via the Newtonian concept of force. More fundamental are momenta, energy and stress. In fact, no one measures force directly. Instead, everytime one says one is measuring a force, a quick rethinking would make one realize that what one really measures is stress (or maybe its gradient). The "force" you feel on your skin, for example, is really your pressure nerve cells picking up a change in pressure. A spring meter measures the tension of the spring, which is really its stress, etc. etc.

In physics, a net force acting on a body causes that body to accelerate (i.e. to change its velocity). Force is a vector. The SI unit used to measure force is the newton.

Force was first described by Archimedes. The total (Newtonian) force on a point particle at a certain instant in a specified situation is defined as the rate of change of its momentum

F = dp/dt = d(mv)/dt

Where m is the inertial mass of the particle, vo is its initial velocity, v is its final velocity, and T is the time from the initial state to the final state; the expression on the right of the equation being the limit as T goes to zero.

Force was so defined in order that its reification would explain the effects of superimposing situations: If in one situation, a force is experienced by a particle, and if in another situation another force is experience by that particle, then in a third situation, which (according to standard physical practice) is taken to be a combination of the two individual situations, the force experienced by the particle will be the vector sum of the individual forces experienced in the first two situations. This superposition of forces, along with the definition of inertial frames and inertial mass, are the empirical content of Newton's laws of motion.

Gravity

Gravitation is the force of attraction that exists between all particles with mass in the universe. It is the force of gravity which is responsible for holding objects onto the surface of planets and, with Newton's law of inertia is responsible for keeping objects in orbit around one another.

"Gravity is the force that pulls you down." -- Merlin in Disney's The Sword in the Stone

Merlin was right, of course, but gravity does much more than just hold you in your chair. It was the genius of Isaac Newton to recognize that. Newton recalled in a late memoir that while he was trying to figure out what kept the Moon in the sky, he saw an apple fall to the ground in his orchard, and he realized that the Moon was not suspended in the sky, but continuously falling, like a cannon ball that was shot so fast that it continuously misses the ground as it falls away due to the curvature of the Earth.

If one wishes to be precise, one should distinguish between gravitation, the universal force of attraction, and gravity, which is the resultant, on the Earth's surface, of the attraction by the earth's masses, and the centrifugal pseudo-force caused by the Earth's rotation. In casual discussion, gravity and gravitation are often used interchangeably.

By Newton's third law, any two objects exert equal and oppositely directed gravitational pull on each other.

Kinetic energy

In physics, kinetic energy is energy possessed by a body by virtue of its motion. In Newtonian mechanics, a body with mass m, moving in a straight line with velocity v, has a translational kinetic energy of

T = m v2/2.

If a body is rotating, its rotational kinetic energy equals

T = I ω2/2.

where I is its moment of inertia and ω its angular velocity.

Where gravity is weak, and objects move at much slower velocities than light (e.g. in everyday phenomena on Earth), Newton's formula is an excellent approximation of relativistic kinetic energy.

Mass

Mass is a property of physical objects which, roughly speaking, measure the amount of matter contained in an object. It is a central concept of classical mechanics and related subjects. In the SI system of measurement, mass is measured in kilograms.

Strictly speaking, mass refers to two quantities:

  • Inertial mass is a measure of an object's inertia, which is its resistance to changing its state of motion when a force is applied. An object with small inertial mass changes its motion more readily, and an object with large inertial mass does so less readily.
  • Gravitational mass is a measure of the strength of an object's interaction with the gravitational force. Within the same gravitational field, an object with a smaller gravitational mass experiences a smaller force than an object with a larger gravitational mass. (This quantity is sometimes confused with weight.)

Inertial and gravitational mass have been experimentally shown to be equivalent, as accurately as we can measure, although they are conceptually quite distinct.

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