Vectors and Scalars Lecture At the end of

Vectors and Scalars Lecture At the end of this lecture you should Understand the difference between a vector and a scalar Have examples of physical quantities represented by vectors and scalars Understand how to add and subtract vectors Know what a resultant vector is Know how to find the change in a vector quantity, calculate relative and resolve a vector into components Understand how vectors can be represented in component form in a coordinate system Be able to do calculations which demonstrate that you have understood the above concepts Have NOTES from this lecture that are legible and useful

Vectors and Scalars Some physical quantities have both size (magnitude) and direction: vectors. Some quantities have only size: scalars.

Vectors can be represented geometrically by arrows

The resultant vector When we add two or more vectors, we get the resultant vector. Here, a + b Note: in lectures and books, vectors are given with an arrow above them or they are written in bold.

Adding more vectors

S - South N - North E - East W - West 15° 15 degrees east of north 45 degrees west of south 45° 30° …..? ….? 30°

Example 1. To find change in a vector quantity A motorcycle moves with a velocity 25 m s-1 due west, then changes to 10 m s-1 due south. Find the change in velocity Δv. Note: you need to state both a magnitude and an angle

Unit vectors x Y Notation for unit vectors: A 5 3 2 - 4 B

Example 2 Find the magnitude of the electric field vector E with components 3i + 4j. What angle does the electric field vector makes with the X-axis.

Example 3. Resolving vectors Resolve this vector along the x and y axes to find its components in the x and y directions respectively.

Example 4. Resultant vector A vector of 15 N at 120º to the x-axis is added to the vector in Example 3. Find the resultant vector.

VAB – velocity of A relative to B VBA – velocity of B relative to A VAE – velocity of A relative to the earth VAB = - VBA Conventional notation for relative motion VAC = VAB + VBC

Example 5. Relative velocity An nomad is looking for his horse and is walking on the Kazakh steppe NE with a speed of 1.56 m s-1 relative to the ground. The horse is running SE with a speed of 6.00 m s-1 relative to the ground. Find the velocity of the horse relative to the nomad.