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Section 2.1 Basics of Motion

How can you tell if something is at rest or in motion? To answer this simple question, you need to look at whether the distance and/or the direction from another object or place is changing with time. That is, we need a way to tell passage of time and a way of measuring distances and indicating directions.

Let's look at them briefly here. You will get into more details as we progress through this book.


To tell the passage of time, we use some repeating phenomenon. The count of repeats gives us a measure of passage of time. For instance, you could use tell passage of time by the number of hartbeats. For longer times, you could count days, or months, etc. A grandfather clock counts periods of a pendulum, a digital wrist watch may count periods of oscillations of a quartz crystal, etc.

Various repeating things have their own repeat times and we need standardization to compare them and to uniquely refer time by the same units. Clocks are devices that count some repeating phenomenon and display the passage of time in some standardized units, such as seconds, minutes, and hours. Since currently, best clocks are based on atomic physics, the unit of second is based on atomic phenomenon. Previously, the unit of second was based on dividing the duration of a day by \(24\times 3600 = 86,400\text{.}\)

National Institute of Standards and Technology (NIST) in USA, has developed cesium-based atomic clocks that measure frequency of the light emitted by a cesium atom. Frequency is the count of repeats in unit time. This frequency is \(9,192,631,770\text{ oscilaltions per second}\text{.}\) Thus, we say that one second is the time it takes for \(9,192,631,770\text{ oscilaltions}\) of this light.

Atomic clocks keep extremely accurate time. As of 2020, they have been reported to tell time within 1/3,000,000 of a second per year, which woudld be 1 part in \(10^{14}\text{.}\) Contrast this precision to a reasonably good Grandfather clock, which may be as good as 1 sec over a 24 hour period - that would give a precision of 1 part in \(86,400\text{.}\) You can visit the NIST website for F2 clock to learn more.

The unit of time most commonly used in physics is seconds, abbreviated by \(\text{s}\) or \(\text{sec}\text{.}\) Smaller times are indicated by using negative powers of \(10\text{.}\) For instance, \(10^{-3}\text{ sec}\) is called a millisecond, denoted by \(\text{msec}\) and \(10^{-6}\text{ sec}\) is called a microsecond, denoted by \(\mu \text{s}\text{.}\) We will study these prefixes in another section.


Distance measurements can be made with your foot, your arm, measureing tape, ruler, mile markers on the road, standard “known” distances of stars, etc. For a long time, a standard meter stick was used to standardize one meter, but that turned out to be not as good as just setting an exact value of speed of light in vaccum, denoted by letter \(c\text{,}\) and then defining one meter by the distance light would travel in \(\dfrac{1}{ 3.00\times 10^{8}}\text{ s}\text{.}\)

\begin{equation*} c = 3\times 10^{8}\text{ m/s}.\ \ \ \ \text{(Exactly!)} \end{equation*}

That is, one meter will be

\begin{equation*} 1\text{ m} = \text{ distance light travels in } \dfrac{1}{ 3\times 10^{8}}\text{ s}. \end{equation*}


Unfortunately, telling direction is not as easy as it sounds. If motion is along a straight line, you can place the motion on the \(x\) axis and indicate direction by using the directions of the positive \(x\) axis and negative \(x\) axis. Thus, if you drive car in the direction of the positive \(x\) axis, your direction of motion will be same as the direction of the postive \(x\) axis, and when you turn around and go in the opposite direction, your direction will be the direction of the negative \(x\) axis.

If motion is in a plane, e.g., on a flat Earth surface or some table, we might use \(xy\) plane of the Cartesian axes for the motion. In this case, we can tell the direction from the origin of the coordinate system by the angle with respect to the positive or negative \(x\) axis.

This is what we do when we tell someone to go \(30^\circ\) North of East direction . By this we mean : (1) I am at the origin, (2) To my East is the positive \(x\) axis, (3) To the North is the positive \(y\) axis, (4) Now, measure \(\theta = 30^{\circ}\) from the direction of \(+x\) axis towards \(+y\) axis. Of course, you do all of this without even thinking about it.

Figure 2.1.1.

If motion is in three-dimensional space, then, we normally use angles \(\theta\) and \(\phi\) of a spherical coordinate system. In the context of direction from the center of Earth, they are also called latitude and longitude, respectively. We will discuss them in a later chapter. Telling direction of stars with respect to Earth is more complicated beacuse Earth is rotating and revolving around the Sun, making the directions of any x,y,z attached to Earth more complicated to follow.

Subsection 2.1.1 All Motion is Relative

Suppose you are driving a car at speed \(30\text{ mph}\) (mph = miles per hour). By this statement, we mean that the car is moving with respect to ground at \(30\text{ mph}\text{.}\) If I asked you a different question: what is the speed of the car with respect to you when you are in the car? Clearly, you are moving with the car and hence the car is not moving with respect to you. Therefore, you will say that speed of the car with respect to you is zero.

This example illustrates that motion is fundamentally relative. That is, whether an object is moving or not, by how much, as well as in which direction, depends on the choice of reference. The reference can be a physical object or just some point in space. The reference is usually taken to be at rest at the origin of a Cartesian cooridnate system and Cartesian coordinates are used for distance and direction.

Figure 2.1.2. The reference object is placed at the origin O of a Cartesian coordinate system. The axes are used to indicate distance and direction of the car.