Lesson 2: Physical Quantities

In this lesson, you will learn about some physical quantities we will be studying in this course, the importance of units, and how to perform unit conversions.

There are 3 learning objectives for this lesson:

1. Differentiate the concepts of position and displacement.
2. Distinguish between the distance traveled by an object and its displacement.
3. Distinguish between vector and scalar quantities.

Fundamental Physical Quantities

The focus of this course is the analysis of motion and forces. In order to describe the various aspects of motion and forces, we have to define some physical quantities. An example of a physical quantity that is likely familiar to you is speed. Speed is simply a measure of how fast or slow something is moving. Other examples of physical quantities include: length, distance, position, displacement, time, velocity, and mass.

Our study of motion and forces has three fundamental physical quantities: Mass, Length, and Time. They are fundamental in that all physical quantities involved in the study of motion and forces can be expressed using these three quantities. For example, speed can be expressed in terms of length and time (miles per hour, kilometers per hour, meters per second, feet per minute are some examples). Volume can be expressed in terms of length cubed.

Each of these fundamental physical quantities are uniquely defined. Over time, these definitions have changed so as to be more precise. For instance, a previous definition of the meter was defined to be one ten millionth of the distance from the north pole to the equator. It is now defined more precisely to be the distance light travels in 1/299,292,458 of a second. The second was defined as 1/86,400 of the mean solar day but now has a more precise, and complex, definition which is related to certain attributes of a cesium-133 atom. Until 2019, the kilogram was defined as the mass of a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France. It is now based on a very precisely measured quantity called Planck’s constant.

In order to perform measurements, every physical quantity has to have a unit associated with it. If you go for your yearly physical in the United States, your height will likely be measured in units of feet and inches and your weight in units of pounds. There are many units of time – seconds, minutes, hours, days, weeks, months, years. Unless a unit is stated, a measured quantity usually does not carry much meaning. Units of measurement can be different depending on the quantity being measured or on one’s location. If you were to go to your yearly checkup in the Britain, your doctor may measure your weight in stones rather than pounds. In most parts of the world, the doctor doesn’t even measure your weight. Instead, the doctor will measure your mass in units of kilograms. You will learn the very important difference between weight and mass in a later lesson.

Since physics is an international endeavor, it is important that a specified set of units is agreed upon and used. This was the point of the development of what we now call SI Units (Système International d’Unités). The beginning of this International System of Units is related to the metric system and the mks system, where mks stands for meter, kilogram, and second. These are the units for the three fundamental physical quantities introduced above.

Length

Length can be further divided into three very specific types: Distance, Position, and Displacement. Distance can be defined as the length measured from one location to another without reference to anything; length in general, or the distance an object travels. If you were to drive from UMass Amherst to Boston following the path below, you would drive a distance of 94.2 miles.

Position is the length measured from one location to a reference point; it is a description of an object’s location. If we wanted to describe the position of the DuBois Library, there are many ways of doing this. We could say that it is located 0.2 miles east of the south athletic field, where the athletic field is the reference point. A more precise way of describing the library’s position is with its latitude and longitude of 42°23’22.9″N 72°31’42.1″W. When describing the position this way, the reference point is 0° latitude, 0° longitude.

The reference point 0° latitude, 0° longitude is similar to the origin on a cartesian coordinate plane. Instead of x and y axes, this coordinate system has the equator and prime meridian as its axes. Interestingly, this “origin” is located in the Atlantic Ocean and marked with a weather buoy. This location is also referred to as Null Island, an imaginary island of 1 m² used for geocoding.

Displacement is the length measured between two reference points; an object’s change in position. So although the drive from UMass to Boston is 94.2 miles, your displacement is actually 74 miles since you are now 74 miles from where you started. An accurate description of your displacement could be something like “74 miles east of UMass”. The expression “as the crow flies” would apply to displacement since a bird is not limited to the roads like a car is. The map below shows the displacement in red but the path traveled in blue. If you had a choice, wouldn’t you take the red path?

What if you drove from UMass to Boston and then back to UMass again? What would your displacement be now?

Vector and Scalar Quantities

In your study of physics you will encounter many concepts that are very similar but have one key difference between them. The key difference between distance and displacement is that they are two different types of physical quantities. These two types of physical quantities are called Scalars and Vectors.

A scalar quantity is a quantity that only describes the magnitude, or amount, of something. The distance from UMass to Boston, 94.2 miles, is a scalar quantity because it only describes the amount of miles you need to drive your car to get to Boston from UMass. There is no information given to describe which direction the car had to travel. If you live in Massachusetts then you probably don’t even have to think about which way to turn when you arrive at the Mass Pike on your way to Boston. If, however, you have never been to Massachusetts, then you may not even know which direction Boston is relative to Amherst (or what the Mass Pike is). What if instead I drop you off in Wellsboro, Pennsylvania and tell you to drive 42.6 miles to Coudersport, Pennsylvania?

Unless you look at a map, you don’t know which way to go. When I tell you to drive 42.6 miles, I am providing you with a scalar quantity. When you look at the map and see that you have to drive 42.6 miles west on route 6, you now have more information. The added information tells you what direction you need to go. When a quantity describes both a magnitude and a direction, it is called a vector quantity.