Vectors and Scalars Objectives: Distinguish between vector and scalar quantitiesDistinguish between vector and scalar quantities Add vectors graphicallyAdd vectors graphically

Scalar – a quantity that can be completely described by a number (called its magnitude) and a unit.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.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.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.Vector quantities can be represented by either letter symbols with arrows above them or with bold letters. d or d Scalars are simply italicized.Scalars are simply italicized.

Vectors are drawn as arrowsVectors 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.An appropriate scale is selected, e.g. 1.0 cm = 25 mi. Draw vectors for the following displacements using the scale above:Draw vectors for the following displacements using the scale above: –125 mi west –50 mi at 45 o east of north

Using a scale of 1.0 cm = 50 km, draw the displacement vector 275 km at 45 o north of west.Using a scale of 1.0 cm = 50 km, draw the displacement vector 275 km at 45 o north of west. Using a scale of ¼ in = 20 mi, draw the displacement vector 150 mi at 22 o east of south.Using a scale of ¼ in = 20 mi, draw the displacement vector 150 mi at 22 o east of south.

Graphical Addition of Vectors Any given displacement can be the result of many different combinations of displacements.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.Resultant vector – the sum of a set of vectors.

To solve a vector addition problem such as one for displacement.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 60 o west of south.Find the resultant displacement of an airplane that flies 20 mi due east, then 30 mi due north, then 10 mi at 60 o west of south.

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