Introducing Physics

Physics is the study of how and why things move. It is also the first modern science and in many ways is the field that we use to exemplify what a science should be. What makes something a science is that practitioners use the scientific method to gain new knowledge in the field.  The scientific method can be expressed in different ways, but the key features are the following:

• Observations of area in question.
• Formulation of hypothesis describing what has been observed.
• Make testable predictions based on the hypothesis.
• Perform experiments to test the predictions.
• Refine theory with new hypothesis.

Thus the main feature of science is that we consider things true because the predictions of our theory have been verified by experiment.  A field in which predictions can not be verified by experiment can not truly be a science.

Physics adds another feature which is that the theories can be written as mathematical expressions.  This makes prediction much easier, but in many sciences it is not the case that the theory can be expressed as a mathematical expression.  In physics this will always be the case, every concept can be expressed as an equation and every equation represents a concept.

Units

Physics is very closely tied to math, but there are important ways in which it is different. One of those ways is that physics describes things in the real world and thus quantities are not just abstract numbers, but refer to real measurable things.  In math we can just talk about the number 4, but in physics you should always ask 4 what?

One way we keep track of this is that numbers in physics should always be associated with units.  We don’t talk about just 4, but instead 4 meters or 4 seconds, 4 dollars or 4 kilograms.  The only case where you should have a number with no units is if you are referring to the actual number of things, like four oranges or four children.

In this class we will use the metric system of units. Why you may not be familiar with the metric system, it is so much better than the English units that are used almost nowhere else in the world aside from the United States.  In the metric system each type of thing you can measure (length, time , mass, energy, etc. ) has only one base unit. You don’t have inches, feet, yards and miles all to express length, there is just one base unit, the meter. Now because sometimes we’d like to measure something very small and sometimes we want to measure things that are very big the metric system has derived units where the base unit is multiplied or divided by some factor of 10.  So to describe very far distances one might use the kilometer or one thousand meters, while to describe something very small one might use the millimeter or one thousandth of a meter.  Once you know the base units and the multipliers you know all the units in the metric system which makes it much simpler than what we use in the United States.

The base units in the metric system can vary in different scientific fields. We will use a very common one called SI units or MKS units.  In this choice the base units for new physical quantities always come from combining meters, kilograms and seconds.  Thus in almost all cases you should convert your units to these three choices where applicable.

Unit Conversion

Since sometimes you may start with a quantity with some units that you want to change it is important to be able to convert between units. Converting between units is easy if you remember one thing. Unit conversion can’t change what you have. So to convert units you multiply by one. Of course if you just multiply by the number one than you won’t do anything, instead you multiply by one in mixed units that cancel out the units you have and replace them with the units you want. For example:

$5 \, hours = 5 \, hours \left({60 \, minutes\over{1\, hour}}\right) = 300 \,minutes$

60 minutes equals one hour so when you multiply by that ratio you are multiplying by one. But the hours cancel and you are left with an answer in minutes.

Estimation

Another important skill to have in physics is the ability to estimate.  This is because when you work out a problem you will make mistakes.  Mistakes are unavoidable, as careful as you may try to be they will still happen.  One of the best ways to catch your mistakes is to estimate the answer to your problem.  An estimation doesn’t have to be exactly right, within a factor of a few is usually good enough.

The key to estimating is to realize you are rather good at estimating the value of quantities as long as you don’t have to be too accurate.  How long is an airplane?  I’m sure you don’t exactly know, and it depends on the plane, but I’m sure you can guess it is less than 500m and more than 10m. So something like 50 to 100 meters is a reasonable estimate.

The other key to estimating is that you can estimate something that you may know nothing about, as long as you can break it down into pieces that you can estimate.  For example you probably don’t know what is the total number of eggs eaten in the United States per year.  But we can estimate a value by breaking the problem down into more manageable bites.  How many eggs to you eat a week? If you think you eat much more or less than most people then try to guess how many eggs other people you know might eat.  Let’s say the answer is 6 eggs a week.  There are 52 weeks in a year so that would be 312 eggs, but let’s round that down to 150 since this is just an estimate.   There are about 300 million people in the US, so that would give us 450 billion eggs consumed a year. A whole lot of eggs.

When you work on physics problems it is a good idea to always estimate what your answer should be.  It won’t be exactly right, but it will help you identify when you have made a mistake. Checking over your work you’ll then often find what you did wrong.