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Lecture 1
What is physics?
Physics, the most fundamental physical science, is concerned with the basic principles of the
Universe. It is the foundation upon which the other sciences— astronomy, biology, chemistry,
and geology - are based. Everything around you can be described by using the tools of physics.
The goal of physics is to use a small number of basic concepts, equations, and assumptions to
describe the physical world. These physics principles can then be used to make predictions about
a broad range of phenomena.
The study of physics can be divided into six main areas:
1. classical mechanics, which is concerned with the motion of objects that are large relative to
atoms and move at speeds much slower than the speed of light;
2. relativity, which is a theory describing objects moving at any speed, even speeds approaching
the speed of light;
3. thermodynamics, which deals with heat, work, temperature, and the statistical behavior of
systems with large numbers of particles;
4. electromagnetism, which is concerned with electricity, magnetism, and electromagnetic
fields;
5. optics, which is the study of the behavior of light and its interaction with materials;
6. quantum mechanics, a collection of theories connecting the behavior of matter at the
submicroscopic level to macroscopic observations.
What is the matter? Let us review briefly a number of historical models of the structure of
matter. The Greek model of the structure of matter was that all ordinary matter consists of
atoms. The atom is a basic unit of matter that consists of a dense central nucleus surrounded by
a cloud of negatively charged electrons (In 1897, J. J. Thomson identified the electron as a
charged particle and as a constituent of the atom). The atomic nucleus (the discovery of the
nucleus in 1911) contains a mix of positively charged protons (scientists determined that
occupying the nucleus are two basic entities, protons and neutrons. and electrically
neutral neutrons (was verified conclusively in 1932). The electrons of an atom are bound to the
nucleus by the electromagnetic force. Protons, neutrons, and a host of other exotic particles are
now known to be composed of six different varieties of particles called quarks, which have been
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given the names of up, down, strange, charmed, bottom, and top. The up, charmed, and top
quarks have electric charges of +2/3 that of the proton, whereas the down, strange, and bottom
quarks have charges of -1/3 that of the proton. The proton consists of two up quarks and one
down quark. the neutron consists of two down quarks and one up quark, giving a net charge of
zero.
The numbers of protons and neutrons in the nucleus of an atom of an element are related to the
atomic mass of the element, which is defined as the mass of a single atom of the element
measured in atomic mass units (u) where 1 u = 1.660 538 7 .10-27 kg.
Motion in One Dimension
Position. A particle’s position is the location of the particle with respect to a chosen reference
point that we can consider to be the origin of a coordinate system. After a particle moves along
the x axis from some initial position xi to some final position xf , its displacement is
(1)
The displacement of a particle is defined as its change in position in some time interval. It is very
important to recognize the difference between displacement and distance traveled. Distance is
the length of a path followed by a particle. Displacement is an example of a vector quantity.
The average velocity of a particle during some time interval is the displacement ∆x divided by
the time interval ∆t during which that displacement occurs:
(2)
The average speed of a particle, a scalar quantity, is defined as the total distance traveled
divided by the total time interval required to travel that distance:
(3)
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The instantaneous velocity of a particle is defined as the limit of the ratio ∆x/∆t. As ∆t
approaches zero. By definition, this limit equals the derivative of x with respect to t, or the time
rate of change of the position:
(4)
The instantaneous speed of a particle is equal to the magnitude of its instantaneous velocity.
The average acceleration of a particle is defined as the ratio of the change in its velocity ∆vx
divided by the time interval ∆t during which that change occurs:
(5)
(a) A car, modeled as a particle, moving along the x axis from A to B has velocity vxi at ti and
velocity vxf at tf . (b) Velocity–time graph (rust) for the particle moving in a straight line. The
slope of the blue straight line connecting A and B is the average acceleration in the time interval
∆t = tf - ti
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The instantaneous acceleration is equal to the limit of the ratio ∆vx /∆t as ∆t approaches
0. By definition, this limit equals the derivative of vx with respect to t, or the time rate of change
of the velocity:
(6)
When the object’s velocity and acceleration are in the same direction, the object is speeding up.
On the other hand, when the object’s velocity and acceleration are in opposite directions, the
object is slowing down. Remembering that F&a is a useful way to identify the direction of the
acceleration.
The equations of kinematics for a particle moving along the x axis with uniform acceleration ax
(constant in magnitude and direction) are:
(7)
Velocity as a function of time
(8)
Position as a function of velocity and time
(9)
Position as a function of time
(10)
Velocity as a function of position
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Freely Falling Objects
An object falling freely in the presence of the Earth’s gravity experiences a free-fall acceleration
directed toward the center of the Earth. If air resistance is neglected, if the motion occurs near
the surface of the Earth, and if the range of the motion is small compared with the Earth’s radius,
then the free-fall acceleration g is constant over the range of motion, where g is equal to 9.80
m/s2. A freely falling object is any object moving freely under the influence of gravity alone,
regardless of its initial motion. Objects thrown upward or downward and those released from rest
are all falling freely once they are released. Any freely falling object experiences an acceleration
directed downward, regardless of its initial motion.
Keep in mind that g is a positive number—it is tempting to substitute - 9.80 m/s2 for g, but
resist the temptation. Downward gravitational acceleration is indicated explicitly by stating the
acceleration as ay = - g.