Force Diagrams

• Newton's First Law (Equilibrium): If the vector sum of all forces in the diagram is zero ($\sum \vec{F} = 0$), the object is in equilibrium. This means it is either at rest or moving with a constant velocity.

• Newton's Second Law (Acceleration): If there is a non-zero net force, the object will accelerate in the direction of that net force. The relationship is defined by the formula $\sum \vec{F} = m \vec{a}$, where $m$ is mass and $\vec{a}$ is acceleration.

• Superposition of Forces: Multiple forces acting on an object can be replaced by a single resultant force. In a diagram, this is achieved by breaking forces into $x$ and $y$ components and summing them independently.

Step-by-Step Construction

• Identify the System: Clearly define which single object is being analyzed and ignore all other objects except for the forces they exert on your chosen system.
• Identify External Forces: List all contact forces (e.g., Tension, Friction, Normal Force) and non-contact forces (e.g., Gravity, Magnetic Force) acting on the object.
• Draw the Vectors: Start all arrows from the center of the object. Ensure the direction is accurate (e.g., gravity always points toward the center of the Earth, regardless of the object's orientation).
• Establish a Coordinate System: Choose an $x$ and $y$ axis that simplifies the math. For objects on an incline, it is often best to align one axis parallel to the surface and the other perpendicular to it.

Force Identification Criteria

• Gravity ($F_g$): Always present if the object has mass; acts vertically downward.
• Normal Force ($F_N$): Exerted by a surface; always acts perpendicular to the surface of contact.
• Friction ($F_f$): Acts parallel to the surface and opposes the relative motion or intended motion.
• Tension ($F_T$): Exerted by strings, ropes, or cables; always pulls away from the object along the line of the rope.

• The 'Perpendicular' Rule: Always check that your Normal Force is exactly $90^{\circ}$ to the surface. A common mistake is drawing it straight up even when the object is on a slope.

• Component Decomposition: If a force (like gravity on a slope) does not align with your chosen axes, immediately draw its components ($F_{gx}$ and $F_{gy}$). This prevents errors when setting up the $\sum F = ma$ equations.

• Check for 'Ghost' Forces: Never include 'Net Force' or 'Centripetal Force' as separate arrows on an FBD. These are the results of other forces, not independent forces themselves.

• Reasonability Check: If an object is known to be at rest, ensure that every force arrow has an opposing arrow or component that cancels it out. If the arrows don't balance, the object must be accelerating.