http://www.ck12.org Chapter 1. What Is Science?
FIGURE 1.
Map of countries not officially using the
metric system worldwide.Students often learn the basics of metric units, but are not fluent in them. Especially in physics, it is important not
just to perform abstract calculations, but to be able to mentally picture what measurements look like.
- How heavy is a 10kg weight?
- How short is someone who is 155cm tall?
The standard unit of length used in physics today is the meter, which is roughly the distance from the tip of your
nose to the end of your outstretched arm. Themeter sticksyou have in your classroom do not have this accuracy.
The standard unit ofmassis the kilogram. A one-kilogram mass corresponds to a weight of approximately 2.
pounds. Mass and weight are not the same property. Weight is the product of the gravitational acceleration,g, and
the mass of the object:W=mg. The corresponding standard weight unit is the Newton, where 4.45 Newtons is
equal to 1 pounds.
The standard unit oftimeis the second, which is familiar to most students.
The standard unit of temperature is the degree Celsius. One degree Celsius is the same as one degree Kelvin, but
they measure from a different starting point. Celsius measures up from the freezing point of water, while Kelvin
measures up from the point called "absolute zero".
These fundamental units are combined intoderived units, such aslengthtime for speed. Speed and velocity have the
derived units oflengthtime. Other derived units include force, energy, voltage, and so forth.
Vectors and Scalars
If we wish to fully define the motion of an object we must state the object’s magnitude and the object’s direction.
In the case of motion, the magnitude is the speed of the object. Quantities such as displacement are represented
by net distance (magnitude) and direction. Any quantity requiring a magnitude and a direction is called avector
quantity. Force is another vector quantity. For example: A 150 N punch (magnitude) to the stomach (direction,
loosely speaking!). Quantities that require only a magnitude for their complete description are calledscalars. Mass
and temperature are examples of scalar quantities.
Dimensional Analysis
Dimensional analysisis the method of using fundamental or standard units in detecting an error and discerning
the correct relationship between physical quantities. As a simple example, recall our old friendd=rt, wheredis
a distance,ris a rate, andtis time. If we accidentally rewrite the equation asr=t/d, we see that the units are
inconsistent since m/s do not equal s/m. If the derived units are not the same on each side of the equation, we know
that a mistake was made. The converse is not true. If the units agree, a mistake may still have been made. (Why?)