Vector Components Coordinates Vectors can be described in

Vector Components

Coordinates ] Vectors can be described in terms of coordinates. • 6. 0 km east and 3. 4 km south • 1 N forward, 2 N left, 2 N up ] Coordinates are associated with axes in a graph. y x = 6. 0 m x y = -3. 4 m

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. Fy Fy = (2. 0 N) sin(60°) = 1. 7 N 60° Fx • x = r cos • y = r sin Fx = (2. 0 N) cos(60°) = 1. 0 N ] This is called projection onto the axes.

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 -dimensional • 3 -dimensional ] The elements, called components, are scalars, not vectors.

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

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. 6 N 2. 1 N 4. 1 N

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. 6 N 2. 1 N q = 27 4. 1 N

Components to Angles ] Find the magnitude and angle of a vector with components x = -5. 0 N, y = 3. 3 N. y y = 3. 3 N x = -5. 0 N L L = 6. 0 N = 33 o above the negative x-axis x

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