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Article Outline
Mechanics, branch of physics concerning the motions of objects and their response to forces. Modern descriptions of such behavior begin with a careful definition of such quantities as displacement (distance moved), time, velocity, acceleration, mass, and force. Until about 400 years ago, however, motion was explained from a very different point of view. For example, following the ideas of Greek philosopher and scientist Aristotle, scientists reasoned that a cannonball falls down because its natural position is in the earth; the sun, the moon, and the stars travel in circles around the earth because it is the nature of heavenly objects to travel in perfect circles. The Italian physicist and astronomer Galileo brought together the ideas of other great thinkers of his time and began to analyze motion in terms of distance traveled from some starting position and the time that it took. He showed that the speed of falling objects increases steadily during the time of their fall. This acceleration is the same for heavy objects as for light ones, provided air friction (air resistance) is discounted. The English mathematician and physicist Sir Isaac Newton improved this analysis by defining force and mass and relating these to acceleration. For objects traveling at speeds close to the speed of light, Newton’s laws were superseded by Albert Einstein’s theory of relativity. For atomic and subatomic particles, Newton’s laws were superseded by quantum theory. For everyday phenomena, however, Newton’s three laws of motion remain the cornerstone of dynamics, which is the study of what causes motion.
Kinetics is the description of motion without regard to what causes the motion. Velocity (the time rate of change of position) is defined as the distance traveled divided by the time interval. Velocity may be measured in such units as kilometers per hour, miles per hour, or meters per second. Acceleration is defined as the time rate of change of velocity: the change of velocity divided by the time interval during the change. Acceleration may be measured in such units as meters per second per second or feet per second per second. Regarding the size or weight of the moving object, no mathematical problems are presented if the object is very small compared with the distances involved. If the object is large, it contains one point, called the center of mass, the motion of which can be described as characteristic of the whole object. If the object is rotating, it is frequently convenient to describe its rotation about an axis that goes through the center of mass. To fully describe the motion of an object, the direction of the displacement must be given. Velocity, for example, has both magnitude (a scalar quantity measured, for example, in meters per second) and direction (measured, for example, in degrees of arc from a reference point). The magnitude of velocity is called speed. Several special types of motion are easily
described. First, velocity may be constant. In the simplest case, the
velocity might be zero; position would not change during the time
interval. With constant velocity, the average velocity is equal to the
velocity at any particular time. If time, t, is measured with a
clock starting at t = 0, then the distance, d, traveled at
constant velocity, v, is equal to the product of velocity and time.
In the second special type of motion,
acceleration is constant. Because the velocity is changing, instantaneous
velocity, or the velocity at a given instant, must be defined. For
constant acceleration, a, starting with zero velocity ( v =
0) at t = 0, the instantaneous velocity at time, t, is
Circular motion is another simple type of
motion. If an object has constant speed but an acceleration always at
right angles to its velocity, it will travel in a circle. The required
acceleration is directed toward the center of the circle and is called
centripetal acceleration (see Centripetal
Force). For an object traveling at speed, v, in a circle of
radius, r, the centripetal acceleration is To understand why and how objects accelerate,
force
and mass
must be defined. At the intuitive level, a force is just a push or a pull.
It can be measured in terms of either of two effects. A force can either
distort something, such as a spring, or accelerate an object. The first
effect can be used in the calibration of a spring scale, which can in turn
be used to measure the amplitude of a force: the greater the force,
F, the greater the stretch, x. For many springs, over a
limited range, the stretch is proportional to the force If an object is motionless, the net force on it
must be zero. A book lying on a table is being pulled down by the earth’s
gravitational attraction and is being pushed up by the molecular repulsion
of the tabletop. The net force is zero; the book is in equilibrium. When
calculating the net force, it is necessary to add the forces as vectors.
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