<meta http-equiv="refresh" content="1; url=/nojavascript/"> Resolving Vectors into Axial Components ( Read ) | Physics | CK-12 Foundation
Dismiss
Skip Navigation

Resolving Vectors into Axial Components

%
Best Score
Practice Resolving Vectors into Axial Components
Practice
Best Score
%
Practice Now
Resolving Vectors into Axial Components
 0  0  0

Resolving Vectors into Axial Components

We know that when two vectors are in the same dimension, they can be added arithmetically.  Suppose we have two vectors that are on a north-south, east-west grid, as shown below.  One of the methods we can use to add these vectors is to resolve each one into a pair of vectors that lay on the north-south and east-west axes. 

Two vectors on a north-south, east-west grid, one originating between north and east, one originating between north and west

The two vectors we are to add is a force of 65 N at 30° north of east and a force of 35 N at 60° north of west.

Sum of two vectors on a north-south, east-west grid, creating a triangle for each vector

We can resolve each of the vectors into two components on the axes lines. Each vector is resolved into a component on the north-south axis and a component on the east-west axis.

Using trigonometry, we can resolve (break down) each of these vectors into a pair of vectors that lay on the axial lines (shown in red above).

The east-west component of the first vector is (65 N)(cos 30° ) = (65 N)(0.866) = 56.3 N east

The north-south component of the first vector is (65 N)(sin 30°) = (65 N)(0.500) = 32.5 N north

The east-west component of the 2 nd vector is (35 N)(cos 60°) = (35 N)(0.500) = 17.5 N west

The north-south component of the 2 nd vector is (35 N)(sin 60°) = (35 N)(0.866) = 30.3 N north

Summary

  • Vectors can be resolved into component vectors that lie on the axes lines.

Practice

Questions

http://www.youtube.com/watch?v=NHnOwJE5Who

  1. What does SohCahToa mean? 
  2. Why is SohCahToa relevant to resolving a vector into components?
  3. Why is the sum of the components larger than the resultant vector?

Review

Questions

  1. A force of 150. N is exerted 22° north of east.  Find the northward and eastward components of this force.
  2. An automobile travels a displacement of 75 km 45° north of east.  How far east does it travel and how far north does it travel?

Image Attributions

Reviews

Email Verified
Well done! You've successfully verified the email address .
OK
Please wait...
Please wait...

Original text