Section 2.1 Basics of Motion
How can you tell if an object is at rest or in motion? To answer this simple question, you need to look at whether the distance and/or the direction of the object from another object or point in space 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. We will get into more details as we progress through this book.
Subsection 2.1.1 Time
Although time is a very abstract concept in physics, it is easy to tell passage of time using clocks. Clocks are just objects or phenomena that repeat themselves. For instance, a hearbeat, a pendulum, the rotating Earth, the motion of Earth around the Sun, etc, are objects/phenomena that repeat naturally. By assuming that duration between repeats is a constant, we can keep track of time by just counting number of repeats between two instants in time. A grandfather clock counts periods of a pendulum, a digital wrist watch may count periods of oscillations of a quartz crystal, etc. For longer times, you could count days, or months, 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, best clocks currently are based on frequency of light emitted in atomic transitions, the unit of second is based on atomic phenomenon. Previously, the unit of second was based on dividing the duration of a day by \(24\times 3600 = 86,400\text{,}\) which turns out to be less accurate than the one based on atomic physics.
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 (https://www.nist.gov/pml/time-and-frequency-division/background-how-nist-f2-works) to learn more.
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www.nist.gov/pml/time-and-frequency-division/background-how-nist-f2-worksThe unit of time most commonly used in physics is seconds, abbreviated by \(\text{s}\) or \(\text{sec}\text{.}\) Shorter 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. for larger units of time we use minutes (1 min = 60 sec), hours (1 hr = 60 min), days (1 day = 24 hr), years (1 yr = 365.25 days), etc.
Subsection 2.1.2 Distance
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*}
\text{Speed of light in vacuum, } 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*}
Subsection 2.1.3 Direction
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 refering the direction of motion to be in the same direction as the direction of the positive \(x\) axis or that of the 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.
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 2.1.4 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 the 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 "object", whether real or fictitious, is usually taken to be at rest at the origin of a Cartesian cooridnate system and Cartesian coordinates with coordinate ticks marked on the axes are used for distance and direction.
