Physics Terminology 1 .

1. Physics Terminology 1. In physics, everyday words that we are familiar with may have special usage and meaning; so we begin our study of physics by learning a few of these terms. Quantity: In everyday usage, the word quantity means the amount of a substance; or how much of a substance we have. In addition to this meaning, quantity in physics refers to anything that we can measure or count. For example, time, length, money, mass, weight, are all quantities because we can measure or count them.

2. Physics Terminology 2. • Measurement:Measurement is the process by which we compare a quantity with a known amount (called a standard) of the same quantity in order to determine how much of the quantity we have. For example, if we want to know the length of our football field, we could lay meter sticks (a meter is our standard for length) along the length of the football field and count how many meter sticks can fit along the length. Of course, this is not practical; so we would use a tape measure which is calibrated in meters to take this measurement.

3. Physics Terminology 3. As we’ve learned so far, quantities are things that we can count or measure in order to determine the amount or size of the quantity. There are certain quantities however, that knowing the amount or size alone does not give a complete description (or information) of the quantity. For example, imagine we are lost at sea and call the Coast Guard to come to our rescue. We tell the Coast Guard that we are 200 miles off the coast of Tampa because that’s all we know. The Coast Guard will have a hard time finding us because they wouldn’t know which way to go to get to us. In light of this, we classify physics quantities into two categories: A scalar quantityneeds only magnitude or size to completely specify it. Examples: money, time, mass, distance, speed. A vector quantityneeds both magnitude and size to completely specify it. Examples: displacement, velocity, force, acceleration.

4. Physics Terminology 4. Aside from classifying quantities as vector or scalar quantities, we also classify quantities into two additional categories as follows: A basic quantityis a quantity that cannot be expressed in terms of other quantities. Examples are length, time and mass. A derived quantity is a quantity that can be expressed in terms of the basic quantities. Examples are volume, area, force, density. There are only 7 basic quantities in physics. The vast majority of quantities are derived quantities. In mechanics, we will encounter 3 basic quantities – length, massandtime. In thermal physics, we will encounter one additional basic quantity – temperature; and in electricity and magnetism, we will encounter an additional basic quantity – electric current. (Note: In older physics textbooks, the electriccharge is considered the basic unit instead of the electric current.)

5. Physics Terminology 5. When we measure quantities, we express the measurements in units. Just as there are basic and derived quantities so are there basic and derived units to go with them. A basic (or base) unit is used to express the measurement of a basic quantity. A derived unit is used to express the measurement of a derived quantity. Worldwide, the quantities (basic and derived) are the same; but the units in which the quantities are expressed used to be (and still are, to a certain extent) different. This created problems for physicists around the globe. To resolve this problem, physicists met in Sèvres, France in 1960 and adopted the SI (Système International d’unités) as the standard for expressing measurements in physics.

6. Physics Terminology 6. The SI System The SI system is a subset of the metric system. The basic quantities and their basic units in the SI system are shown in the table below: The SI system is often referred to as the mks system (m = meter, k = kilogram, s = seconds).

7. Physics Terminology 7. The Metric System The metric system is quite easy to use because the units are in multiples of 10. The table below shows some of the commonly used units, their prefixes and their relationship to the standard unit (meter in the table) in powers of 10.

8. Physics Terminology 8. In the example where we were lost at sea and called the Coast Guard for help we saw that it was necessary that we give the Coast Guard a direction in addition to the distance from shore in order for them to rescue as in a timely manner. Equally important is a reference point from which the distance from shore is measured; which in our case is the Coast of Tampa (quite vague but okay for now). This takes us to the idea of a • Frame of Reference: (In simple terms, it is) a set of axes which serves as a reference for taking measurements. For us in beginning physics, a reference frame is just a convenient set of coordinate axes that we choose as references for taking our measurements.

9. Kinematic Quantities Distance versus Displacement Constant Speed versus Constant Velocity Average Speed versus Average Velocity Instantaneous Speed versus Instantaneous Velocity Acceleration

10. Displacement: The straight line distance pointing in the direction from start to finish. Displacement is a vector quantity. Distance: The total distance traveled from start to finish. Distance is ascalar quantity. Questions: In the figure, how do the displacements of cars A (the blue car) and car B (the orange/red) compare? How do the distances traveled by the two cars compare?

11. Position Vector:The location of an object relative to the origin. Displacement Vector: The location of an object relative to a reference point (not necessarily the origin). Questions: Can you name some position vectors in the figure? What about some displacement vectors? Is it correct to say that the position vector is also a displacement vector? Explain. Position Vector versus Displacement Vector

12. We can say that a vector is a directed distance. We write vectors in several ways: • We write the starting point followed by the endpoint letters and draw an arrow over them. For example the position vector from the origin to point A is written (pronounced vector OA). The displacement vector from A to C is written as . • The vector is denoted by just one letter with an arrow over it. For example, we can label the distance OA as A (as in diagram) and write as . • In print, a vector is denoted in boldface type, for example OA or A • When we draw vectors, the length of the vector represents its magnitude (or size) and the arrow represents its direction. • Questions: • Name some vectors in the diagram. • Can you say that ACCA, OAAO? Explain why or why not. Vector Notation and Basic Vector Properties A

13. We see from the previous slide that as far as distance is concerned, OAAO; but for vectors, OAAO. We also note in the figure that if we want to find the total distance traveled by car B, all we need to do is add the segments traveled together. Thus we write (for car B) . We’ve already seen that this total distance traveled by car B is not the same as the displacement of car B. Our question then is: Can vectors be added together? Is there a special rule for adding and subtracting vectors? The answer to both questions is yes. When we add (or subtract) vectors, we get a new vector called the resultant. There are two ways of adding vectors together (described on the next slide): The graphical Method The Analytic or Component method. The negative of a vector is a vector having the same length but opposite direction. Subtracting a vector is the same as adding the negative of the vector being subtracted. Vector Properties and Basic Vector Math A

14. Vector Addition/Subtraction – Graphical Method 1 The picture below shows how vectors are added together by the graphical method. The tail (starting point) of the second vector is attached to the head (end point or the arrow) of the first vector. If there are more than two vectors, the process continues until all the vectors are joined together. The result of this addition is a vector, called the resultant, from the tail of the first vector to the head of the last vector attached. The graphical method is also known as the Head-to-Tail or Tip-to-Tail method. Head (or Tip) Tail

15. Vector Addition/Subtraction – Graphical Method 2 We have seen that the negative of a vector is a vector having the same length but pointing in the opposite direction. Using this definition, we can easily perform vector subtraction by adding the negative of the vector to be subtracted, since A (B)A B.

16. Resolving Vectors into Components-1 We have been able to add two vectors together to obtain a resultant vector. The question now is : Can we undo vector addition? In other words, if we know the resultant vector, can we obtain two vectors that add up to give the resultant. The answer is yes. As a matter of fact, there are numerous possibilities depending on our frame of reference. The figure on the next slide shows a few possibilities. Note in the figure that the two vectors being added form the sides of a parallelogram – hence vector addition by the graphical method is often referred to as the Parallelogram Method of Vector Addition. • The process of breaking up a vector into two or more vectors that add up to give the original vector is referred to as vector resolution(or resolving vectors into components); and the “broken-up” vector pieces are called components.

17. Resolving Vectors into Components-2

18. Resolving Vectors into Components-3 Among the numerous sets of axes that we can choose as our frame of reference, our preference in this course is the familiar - (Cartesian) coordinate axes. A given vector, A, is resolved into and components as shown in the figure below. Ax is the x-component Ay is the y-component

19. Vector Addition by the Component Method The figure below illustrates how vectors are added by the component method. First resolve the vectors to be added into components. Then add the -components of all the vectors together to find the -component of the resultant. Do likewise for the -component. Use the Pythagorean theorem to find the magnitude of the resultant; and the arctangent function to find its direction.

20. Multiplying a Vector by a Scalar When a vector quantity, G, is multiplied by a scalar quantity, , the result is a new vector, H, whose magnitude is n times the magnitude of G and whose direction is the same direction as G. H = G

21. Unit Vectors-1 The concept of a unit vector is convenient in working with vectors. A unit vector has a magnitude of 1 unit and points in the direction of the given vector.The notation for a unit vector is usually a lowercase letter with a hat over it. As an example, vector R and a unit vector in the direction of R are shown below. Thus a vector can be expressed as its magnitude (a scalar) multiplied by the unit vector in the vector’s direction. For the above vector, we write Therefore, we define the unit vector as

22. Unit Vectors -2 • Vector B in the figure can be written in terms of unit vectors as • Unit vectors directed along the co-ordinate axes are of particular interest. They are denoted by and as shown in the figure.

23. Unit Vectors -2 • In 3- dimensional space, a third unit vector, , is introduced in the z-direction as shown in the figure. • Vector Rin the figure can be written in terms of unit vectors as

24. Average speed: The total distance traveled divided by the time taken to travel that distance. In symbols Average velocity: The displacement divided by the time taken to travel that displacement. In symbols Question: What is the difference between the two formulas above? Average speed and average velocity