Free Body Diagrams

Step 1: Identify the System: Clearly define which object you are analyzing and ignore all forces that do not act directly upon it.

Step 2: Identify Interactions: List all contact forces (like friction or tension) and non-contact forces (like gravity or magnetism) acting on the body.

Step 3: Establish a Coordinate System: Choose an x-y axis that aligns with the expected direction of motion or acceleration to simplify vector resolution.

Step 4: Draw and Resolve: Draw the vectors and, if a force acts at an angle, resolve it into horizontal and vertical components using trigonometry ($F_x = F \cos \theta$, $F_y = F \sin \theta$).

The Gravity Check: Always start by drawing the weight vector ($W = mg$) pointing vertically downward, regardless of the surface orientation.

Normal Force Orientation: Ensure the normal force is always drawn perpendicular to the surface of contact, not necessarily opposite to gravity.

Resultant Force Verification: If the object is at rest or moving at a constant velocity, the vector sum of all arrows must be zero; if it is accelerating, the arrows must show a clear imbalance in the direction of acceleration.

Common Mistake: Never include 'velocity' or 'acceleration' as arrows on an FBD; only actual physical forces belong on the diagram.

Centripetal Force Error: Students often mistakenly add 'centripetal force' as an extra arrow. In reality, centripetal force is the resultant of other forces (like tension or friction) acting toward the center, not a separate force itself.

Action-Reaction Confusion: Do not include the force the object exerts back on the surface. For example, if a book sits on a table, only the table's push on the book (Normal Force) goes on the book's FBD.

Friction Direction: Friction always opposes the relative motion or the tendency of motion between surfaces; it is always parallel to the contact surface.