Free Body Diagrams (College Board AP® Physics 1: Algebra-Based)

Free-body diagrams

Properties of free-body diagrams

• Free-body diagrams can be used to:

  • identify which forces act in which plane

  • determine the resultant force 

• Forces are vector quantities that describe the interactions between objects or systems

• The free-body diagram of an object or system uses arrows to show each of the forces exerted on the object by the environment

  • The length of the arrow represents the magnitude of the vector

  • The direction of the arrow represents the direction of the vector

  • The length of the arrows must be proportional to their magnitudes

• Each force arrow is labelled with either:

  • a description of the type of force acting and the objects interacting with clear cause and effect, e.g. the gravitational pull of the Earth on the ball

  • the name of the force, e.g. Weight

  • an appropriate symbol, e.g.

Examples of forces exerted on objects

• A system is treated as though all of its mass is located at the center of mass

  • The forces exerted on an object or system are represented as vectors originating from their center of mass

Free-body diagram of a suspended object

Free-body diagram of object moving on rough surface

Using a coordinate system

• A coordinate system simplifies the translation from a free-body diagram to an algebraic representation

• One plane of the coordinate system is parallel to the direction of acceleration

• A coordinate system consists of:

  • two axes perpendicular to each other

  • a positive direction that is opposite to the negative direction

A coordinate system applied to an object moving on a rough surface

• It is common for the x and y axes to form part of the coordinate system

• Using a coordinate system is a useful way to measure the angles of forces

  • Angles can be measured from either axis

  • This is explained in the revision note Combining vectors

A coordinate system applied to an object with a force at an angle

Inclined Planes

• In a free-body diagram of an object on an inclined plane, it is useful to set one axis parallel to the surface of the incline

  • An inclined plane, or a slope, is a flat surface tilted at an angle,

• The angles of each of the vectors can then be measured from the inclined plane and the magnitude resolved

  • Instead of thinking of the component of the forces as horizontal and vertical, it is easier to think of them as parallel or perpendicular to the slope

• The weight of the object acts vertically downwards and the normal (or reaction) force, always acts vertically upwards from the object on the slope

• The normal (or reaction) force, always acts upwards perpendicular to the slope

  • Remember the equation for weight

• The weight force, , is a vector and can be split into the following components:

  • perpendicular to the slope

  • parallel to the slope

• If there is no friction, the force causes the object to move down the slope

• If the object is not moving perpendicular to the slope, the normal force will be

Forces on inclined planes