Free Body Diagram Title

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This text is meant to accompany class discussions. It is not everything there is to know about the forces. It is meant as a  prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)

Fill out this summary sheet as after reading each section, (click here). (Your teacher may give you a Google Apps link instead.

Going from Diagram to Math Equations


The free body diagrams that you will create are math equations in picture form. By following some simple rules, you can typically create two equations for each free body diagram. These rules are not absolute. But they are designed to make the equations shorter and simpler.

PushPin Identify a coordinate system that has x and y being perpendicular to each other.
PushPin Choose a coordinate system that is parallel and perpendicular to the net force. If the net force equals zero , then make the coordinate system parallel to the surface.
PushPin To create an equation add up all the vectors that are pointing in the same line. With an x and y coordinate system, you will two lines perpendicular to each other.
PushPin All the vectors that point in one direction are positive. Vectors that point in the opposite direction are negative. You choose what is positive and negative.
PushPin The math is easier and the questions are generally shorter if the net acceleration's direction is made to be positive.


These two examples will show how these rules work.

Example 1: Creating a Pair of Equations from a Free Body Diagram

This YouTube video can be seen here,


Example 2: Creating a Pair of Equations from Another Free Body Diagram

This video can be viewed on YouTube at


Example 3: Creating a Pair of Equations from a Third Free Body Diagram

Example 4


Example 5 Moving at a Constant Velocity

This video show the setup for a box on an incline that is moving at with a constant velocity. This video is a more complete solution than above.

This YouTube video is available here too,


Example 6: Moving with a Net Acceleration

This video shows the setup for a box on an incline that is moving at with a net acceleration.

This video can also be found on YouTube at



Answer the questions below after viewing the videos above. They refer to this free body diagram.

Reference Free body diagram


1 Why is the ΣF in the x-direction equal to manet and not zero?
2 Why are the xy coordinates rotated?
3 Why is the ΣF in the y-direction equal to zero?
4 Why is the frictional force negative?

5 Why is the sign of "mgsinθ" positive?
6 How come there isn't a tension force in the free body diagram?



by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)