1. Vector Components

2. Coordinates  Vectors can be described in terms of coordinates. 6.0 km east and 3.4 km south6.0 km east and 3.4 km south 1 N forward, 2 N left, 2 N up1 N forward, 2 N left, 2 N up  Coordinates are associated with axes in a graph. y x x = 6.0 m y = -3.4 m

3. Use of Angles  Find the components of vector of magnitude 2.0 N at 60° up from the x-axis.  Use trigonometry to convert vectors into components. x = r cos  y = r sin   This is called projection onto the axes. FyFy FxFx F x = (2.0 N) cos(60°) = 1.0 N F y = (2.0 N) sin(60°) = 1.7 N 60°

4. Ordered Set  The value of the vector in each coordinate can be grouped as a set.  Each element of the set corresponds to one coordinate. 2-dimensional2-dimensional 3-dimensional3-dimensional  The elements, called components, are scalars, not vectors.

5. Component Addition  A vector equation is actually a set of equations. One equation for each componentOne equation for each component Components can be added like the vectors themselvesComponents can be added like the vectors themselves

6. Vector Length  Vector components can be used to determine the magnitude of a vector.  The square of the length of the vector is the sum of the squares of the components. 4.1 N 2.1 N 4.6 N

7. Vector Direction  Vector components can also be used to determine the direction of a vector.  The tangent of the angle from the x-axis is the ratio of the y-component divided by the x-component. 4.1 N 2.1 N 4.6 N 

8. Components to Angles  Find the magnitude and angle of a vector with components x = -5.0 N, y = 3.3 N. y x x = -5.0 N y = 3.3 N  = 33 o above the negative x-axis L  L = 6.0 N

9. Alternate Axes  Projection works on other choices for the coordinate axes.  Other axes may make more sense for a particular physics problem. next y’ x’   