Lecture # 02 scalar and vector quantities.pptx

scalar and vector quantities

1. Lecture No 02 Applied Physics Course: Applied Physics. 1

2. Contents Scalar Vector Parallel and Antiparallel vectors Addition of vectors Components of a vector Course: Applied Physics. 2

3. Scalar A quantity which is completely specified by a certain number associated with a suitable unit without any mention of direction in space Examples of scalar quantities are time, mass, length, volume, density, temperature, energy, distance, speed etc. The number describing the quantity of a particular scalar is known as its magnitude. The scalars are added subtracted, multiplied and divided by the usual arithmetical laws. Course: Applied Physics. 3

4. vectors A quantity which is completely described only when both their magnitude and direction are specified is known as vector. Examples of vector are force, velocity, acceleration, displacement, torque, momentum, gravitational force, electric and magnetic intensities etc. A vector is represented by a Roman letter in bold face Its magnitude by the same letter in italics. Thus, V or means vector and V=| | is magnitude of the vector.   Course: Applied Physics. 4

5. Representation of vectors A vector is represented by boldface letter in italic with arrowhead above it i.e., The arrowhead reminds that vector has a direction A vector is always drawn as a line with arrowhead The length of the line represents the magnitude of the vector, and the arrow shows the direction of that vector   Course: Applied Physics. 5

6. Parallel & antiparallel vectors Parallel Vectors If two vectors have the same direction, then they are said to be parallel vectors Parallel vectors must have the same direction but may have different magnitudes Antiparallel Vectors If two vectors have the exact opposite direction, then they are said to be antiparallel vectors Antiparallel vectors have the opposite direction but may have different magnitudes Course: Applied Physics. 6

7. Negative vector A vector having the same magnitude as that of original vector ( ) but exactly opposite direction is known as negative of a vector ( ) The magnitude, or length, of a vector, cannot be negative; it can be either be zero or positive. The negative sign is used here to indicate that the vector has the opposite direction of the reference vector.   Course: Applied Physics. 7

8. Vector addition using head to tail rule The head-to-tail method is a graphical way to add vectors The tail of the vector is the starting point of the vector, and the head (or tip) of a vector is the final, pointed end of the arrow. Steps for using Head to Tail Rule for Vectors Addition: Chose a suitable scale Draw an arrow (having the correct length as per selected scale and correct direction) to represent the first vector Now draw an arrow to represent the second vector If there are more than two vectors, continue this process for each vector to be added. Draw an arrow from the tail of the first vector to the head of the last vector. This is the resultant, or the sum, of the other vectors. Course: Applied Physics. 8

9. Vector addition using head to tail rule Course: Applied Physics. 9

10. Vector addition using head to tail rule Course: Applied Physics. 10

11. EXAMPLE Question: Use the graphical technique for adding vectors to find the total displacement of a person who walks the following three paths (displacements) on a flat field. First, she walks 25.0 m in a direction north of east. Then, she walks 23.0 m heading north of east. Finally, she turns and walks 32.0 m in a direction south of east. Solution: Represent each displacement vector graphically with an arrow, labeling the first A ,the second B , and the third C , making the lengths proportional to the distance and the directions as specified relative to an east-west line. The head-to-tail method outlined above will give a way to determine the magnitude and direction of the resultant displacement, denoted R.   Course: Applied Physics. 11

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17. Vector subtraction Course: Applied Physics. 17

18. Components of a vector Consider a rectangular (cartesian) coordinate system of axes as shown in figure We then draw the vector with its tail at O, the origin of the coordinate system. We can represent any vector lying in the xy -plane as the sum of a vector parallel to the x-axis and a vector parallel to the y-axis. These two vectors are labeled and in Fig. 1.17a; they are called the component vectors of vector and their vector sum is equal to . In symbols   Course: Applied Physics. 18

19. Components of a vector Since each component vector lies along a coordinate-axis direction, we need only a single number to describe each one. When points in the positive x-direction, we define the number to be equal to the magnitude of .When points in the negative x-direction, we define the number to be equal to the negative of that magnitude (the magnitude of a vector quantity is itself never negative). We define the number in the same way. The two numbers and are called the components of   Course: Applied Physics. 19

20. Components of a vector Course: Applied Physics. 20

21. Components of a vector Course: Applied Physics. 21

22. Components of a vector Course: Applied Physics. 22

23. Components of a vector Course: Applied Physics. 23

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