Units of Measurement
1. Measurement is very important in physics. Every measurement — a distance, a weight, an interval of time, etc, requires two things: a number and a unit. We nay, for example, obtain as the result of the measurement of different distances, 20 feet, 5 miles, or as the result of the measurement of different weights, 6 pounds, 25 tons, 4 ounces, or as the result of the measurement of different time intervals, 7 hours, 26 seconds, etc. As the result of an experiment we may get the measurements, 10 calories, 90 horsepower, 6 volts, 12 kilowatts, etc. In each case, the unit is as essential as the number which expresses the amount.
2. Although there are numerous different units, we can express each unit in terms of not more than three special units. These three fundamental units are the units of length, mass, and time. All other units are derived units, as we can always write them as some combination of the three fundamental units.
3. There are in general two sets of fundamental units: a) the metric, b) the English. Throughout the world, scientists express scientific observations nearly always in terms of metric units. This set uses the standard meter as the unit of length, the standard kilogram as the unit of mass, and the second as the unit of time. The standard meter is a platinum-iridium bar. It has 100 equal parts, centimeters.
4. To measure large distances it is convenient to use large units of length. Such units arc the kilometer in the metric system and the mile in the English system. One kilometer is equivalent to 1000 meters, and one mile is equivalent to 5280 ft (feet).
5. Astronomers recognize three kinds of time: first, sidereal time; second, apparent solar time; and third, mean solar time. We use the last in everyday life. For several reasons (one is that the earth’s orbit is elliptical), the apparent solar day varies slightly from day to day. An apparent solar day in December is about one minute longer than an apparent solar day in September.
6. The average length of all apparent solar days throughout a solar year is the mean solar day. For astronomical purposes, we use a different time scale, sidereal time. There is one more sidereal day in one solar year than there are mean solar days.
Gravity and Falling Bodies
1. In the absence of friction, ail bodies, large and small, fall with the same acceleration. This law of falling bodies is a physical paradox for it contradicts the conclusion a person may come to from general observations. There is nothing to wonder at, for centuries ago the great philosopher Aristotle taught that heavy bodies fall' proportionately faster than lighter bodies.
2. After nealy 2000 years, in the year 1590 Galileo- was thinking over the question of falling bodies. He found apparent inconsistencies in Aristotle’s teachings. At tests, he dropped various kinds of objects from different levels of the leaning tower of Pisa and timed their fall and measured their velocities.
3. Once Galileo attracted a lot of people to the leaning tower. From the top of the tower he dropped two- stones, one large and one small. These two bodies fell side by side and struck the ground together. That was the beginning of a new era in science. The importance of Galileo’s many experiments is not in the fact that they demonstrated the mistakes in Aristotle’s 'reasoning, but that they gave the world a new scientific method, the method of experimentation.
4. It is easy to repeat Galileo’s experiment. Take a coin and a small piece of paper and drop them simultaneously from the same height to the floor. The coin will fall down fast, while the piece of paper will be in the air for a much longer period of time. If you crumple the piece of paper and roll it into a little ball, it will fall almost as fast as the coin. But if you have a long glass cylinder evacuated of air, you will see that a coin and an uncrumpled piece of paper will fall inside the cylinder at exactly the same speed.
5. The next step that Galileo took in the study of falling bodies was to find a mathematical relation between the time which the fall takes and the distance which it covers. Since the free fall is too fast and the human eye cannot observe it in detail, and since Galileo did not have such modern devices as fast movie cameras he let the balls of different materials roll down an inclined plane instead of falling straight down. To measure time he used a water clock, a device with a spigot that could be turned on and off. Galileo worked the successive position of the objects which were rolling down an inclined plane at equal intervals of time.