Vectors and ScalarsVectors and ScalarsObjectives:•Distinguish between vector and scalar quantities•Add vectors graphically

• Scalar – a quantity that can be completely described by a number (called its magnitude) and a unit.– Ex: length, temperature, and volume

• Vector – a quantity that requires both magnitude (size) and direction.– Displacement, force, and velocity

• Displacement – the net change in position of an object; or the direct distance and direction it moves.– Examples: 15 mi NE, 10 meters upward– It does not contain any information about the

path an objects moves.– How can an object change position but have a

displacement of zero? Give an example.

• Vector quantities can be represented by either letter symbols with arrows above them or with bold letters.

d or d

• Scalars are simply italicized.

• Vectors are drawn as arrows– in the correct direction– and the magnitude is indicated by the length.

• An appropriate scale is selected, e.g. 1.0 cm = 25 mi.

• Draw vectors for the following displacements using the scale above:

– 125 mi west– 50 mi at 45o east of north

• Using a scale of 1.0 cm = 50 km, draw the displacement vector 275 km at 45o north of west.

• Using a scale of ¼ in = 20 mi, draw the displacement vector 150 mi at 22o east of south.

Graphical Addition of VectorsGraphical Addition of Vectors

• Any given displacement can be the result of many different combinations of displacements.– For example, there is more than one way to

get to the cafeteria.• Resultant vector – the sum of a set of

vectors.

• To solve a vector addition problem such as one for displacement.1. Choose a suitable scale and calculate the scale length of each

vector.

2. Draw a north-south reference line. Graph paper can be used.

3. Using a ruler and protractor, draw the first vector and then draw the other vectors so that the initial end of each vector is placed at the terminal end of the previous vector.

4. Draw the sum, or the resultant vector, from the initial end of the first vector to the terminal end of the last vector.

5. Measure the length of the resultant and use the scale to find the magnitude of the vector. Use a protractor to measure the angle of the resultant.

• Find the resultant displacement of an airplane that flies 20 mi due east, then 30 mi due north, then 10 mi at 60o west of south.

• Find the resultant of the displacements 150 km due west, then 200 km due east, and then 125 km due south.