Reference
Book is
• Physics and Measurement
Standards of Length, Mass, time and
Dimensional Analysis
• The laws of physics are expressed in
terms of basic quantities that require a
clear definition.
• In mechanics, the three basic quantities
are length (L), mass (M), and time (T).
All other quantities in mechanics can be
expressed in terms of these three.
In 1960, an international committee
established a set of standards for length,
mass, and other basic quantities. The system
established is an adaptation of the metric
system, and it is called the SI system of units.
(The abbreviation SI comes from the
system’s French name “Système International.”) In this system, the units of length,
mass, and time are the meter, kilogram, and
second, respectively [Kms]
Length
As recently as 1960, the length of the meter was
defined as the distance between two lines on a specific
platinum – iridium bar stored under controlled
conditions in France. This standard was abandoned for
several reasons, a principal one being that the limited
accuracy with which the separation between the lines
on the bar can be determined does not meet the
current requirements of science and technology.
In the 1960s and 1970s, the meter was defined as
1 650 763.73 wavelengths of orange-red light emitted
from a krypton-86 lamp. However, in October 1983, the
meter (m) was redefined as the distance travelled by
light in vacuum during a time of 1/299 792 458 second.
Mass
The basic SI unit of mass, the
kilogram (kg), is defined as the
mass of a specific platinum –
iridium alloy cylinder kept at the
International Bureau of Weights
and Measures at Sèvres, France.
This
mass
standard
was
established in 1887 and has not
been changed since that time
because platinum–iridium is an
unusually stable alloy
Time
Before 1960, the standard of time was defined in terms of
the mean solar day for the year 1900.2 The mean solar
 1  1  1 
second was originally defined as  60   60   24  of a mean solar
day. The rotation of the Earth is now known to vary
slightly with time, however, and therefore this motion is
not a good one to use for defining a standard.
Thus, in 1967 the SI unit of time, the second, was
redefined using the characteristic frequency of a
particular kind of cesium atom as the “reference clock.”
The basic SI unit of time, the second (s), is defined as 9
192 631 770 times the period of vibration of radiation
from the cesium-133 atom
DIMENSIONAL ANALYSIS
In solving problems in physics, there is a useful
.
and powerful procedure called dimensional
analysis. Dimensional analysis makes use of the
fact that dimensions can be treated as algebraic
quantities.
• quantities can be added or subtracted only if
they have the same dimensions.
• Furthermore, the terms on both sides of an
equation must have the same dimensions.
Let us use dimensional analysis to check
the validity of this expression. x  1 a t 2
2
The quantity x on the left side has the dimension
of length L. We can perform a dimensional check
by substituting the dimensions for acceleration,
L/T2, and time, T, into the equation. That is, the
1
dimensional form of the equation x  a t 2
2
is
The units of time squared cancel as shown, leaving the
unit of length.
CONVERSION OF UNITS
Sometimes it is necessary to convert units from
one system to another. Conversion factors
between the SI units and conventional units of
length are as follows:
EXAMPLE 1.1 Analysis of an Equation
Show that the expression v = at is dimensionally
correct, where v represents speed, a
acceleration, and t a time interval.
EXAMPLE 1. 2 Analysis of a Power Law
Suppose we are told that the acceleration a of
a particle moving with uniform speed v in a
circle of radius r is proportional to some power
of r, say rn, and some power of v, say vm. How
can we determine the values of n and m?
The Laws of Motion
•The Concept of Force
•Newton’s First Law and Inertial
Frames
•Newton’s Second Law
•The Force of Gravity and Weight
•Newton’s Third Law
•Some Applications of Newton’s Laws
•Forces of Friction
THE CONCEPT OF FORCE
In these examples, the word force
is associated with muscular
activity and some change in the
velocity of an object. Forces do
not always cause motion,
however. For example, you can
push (in other words, exert a
force) on a large boulder not be
able to move it. If the net force
exerted on an object is zero, then
the acceleration of the object is
zero and its velocity remains
constant.
What force (if any) causes the
Moon to orbit the Earth?
Newton answered this by stating
that forces are what cause any
change in the velocity of an object.
Therefore, if an object moves with
constant velocity, no force is
required for the motion to be
maintained. The Moon’s velocity is
not constant because it moves in a
nearly circular orbit around the
Earth. We now know that this
change in velocity is caused by the
force exerted on the Moon by the
Earth.
•Newton’s First Law and Inertial Frames
Before about 1600, scientists felt that the natural state of
matter was the state of rest. Galileo was the first to take a
different approach to motion and concluded that it is not
the nature of an object to stop once set in motion: rather,
it is its nature to resist changes in its motion. In his words,
“Any velocity once imparted to a moving body will be
rigidly maintained as long as the external causes of
retardation are removed.” This approach was later
formalized by Newton in Newton’s first law of motion:
In the absence of external forces, an object at rest
remains at rest and an object in motion continues
in motion with a constant velocity (that is, with a
constant speed in a straight line).
NEWTON’S SECOND LAW
Newton’s second law answers the question of what
happens to an object that has a nonzero resultant force
acting on it.
m1
F1
(A)
2F1
a1
m1
F2
(B) F1
(C)
a2 = 2a1
1/2 F1
From such observations, we conclude that the
acceleration of an object is directly proportional to the
resultant force acting on it.
m1
F
(A)
2m1
a1
m2
F
(B) m1
(C)
a2 = 2a1
1/2 m1
From such observations, we conclude that the
acceleration of an object is inversely proportional to its
mass.
These observations are summarized in
second law:
Newton’s
The acceleration of an object is directly
proportional to the net force acting on it and
inversely pro-portional to its mass.
The SI unit of force is the Newton, which is
defined as the force that, when acting on a 1kg mass, produces an acceleration of 1 m/s2.
In the British engineering system, the unit of
force is the pound, which is defined as the force
that, when acting on a 1-slug mass produces an
acceleration of 1 ft/s2:
A hockey puck having a mass of
0.30 kg slides on the horizontal,
frictionless surface of an ice rink.
Two forces act on the puck, as
shown in Figure. The force F1 has
a magnitude of 5.0 N, and the
force F2 has a magnitude of 8.0 N.
Determine both the magnitude
and the direction of the puck’s
acceleration.
The resultant force
in the x direction is
The resultant force
in the y direction is
Now we use Newton’s
second law in component
form to find the x and y
components of acceleration:
The acceleration has a
magnitude of
and its direction relative
to the positive x axis is
NEWTON’S THIRD LAW
This simple experiment illustrates a general principle of
critical importance known as Newton’s third law:
If two objects interact, the
force F12 exerted by object 1 on
object 2 is equal in magnitude
to and opposite in direction to
the force F21 exerted by object
2 on object 1:
In reality, either force can be labeled the action or
the reaction force. The action force is equal in
magnitude to the reaction force and opposite in
direction. In all cases, the action and reaction
forces act on different objects
why does the TV
not accelerate in the
direction of Fg ?
What is happening is that
the table exerts on the TV
an upward force n called
the normal force.
The normal force is a contact force that prevents
the TV from falling through the table and can have
any magnitude needed to balance the downward
force Fg