📖 In-Depth Theory
What Is a Free Body Diagram?
A FREE BODY DIAGRAM (FBD) shows all the forces acting ON a single object, drawn as arrows from (or through) the object.
RULES:
Arrow length ∝ force magnitude.
Arrow direction = direction of force.
Label each force with its type AND magnitude (if known).
Draw forces from the centre of mass or contact point.
Include ALL forces — weight, normal contact, friction, tension, drag, upthrust, applied forces.
COMMON FORCES TO SHOW:
WEIGHT (W): always downward, from centre of mass.
NORMAL CONTACT FORCE (N): perpendicular to the surface, away from surface.
FRICTION: along the surface, opposing motion (or tendency to move).
DRAG / AIR RESISTANCE: opposing motion, in fluid.
TENSION: along string/rope/rod, towards the attachment point.
UPTHRUST: upward, in a fluid.
THRUST/ENGINE FORCE: direction of motion.
Interpreting Free Body Diagrams
BALANCED FORCES (resultant = 0):
If all force arrows cancel out → object in EQUILIBRIUM.
Object either stationary OR moving at constant velocity (Newton's 1st Law).
UNBALANCED FORCES (resultant ≠ 0):
Net force in one direction → object ACCELERATES in that direction (Newton's 2nd Law).
EXAMPLES:
Book on a table: weight down = normal contact force up → balanced → stationary.
Car accelerating: thrust > drag → net forward force → accelerates.
Sky diver in free fall: weight down, drag up. Initially weight > drag → accelerates down. At terminal velocity: weight = drag → balanced → constant velocity.
Box pushed on rough surface: applied force forward, friction backward → if equal → constant velocity.
FINDING RESULTANT FROM FBD:
Add all force vectors (tip-to-tail or by resolving into components).
If forces are not at right angles, use scale drawing or trigonometry.
Resolving Forces from Free Body Diagrams
When forces act at angles, resolve them into HORIZONTAL and VERTICAL COMPONENTS.
FOR A FORCE F AT ANGLE θ TO HORIZONTAL:
Horizontal component: Fx = F cos θ
Vertical component: Fy = F sin θ
This allows calculation of resultant in each direction separately.
EQUILIBRIUM using components:
Sum of horizontal forces = 0
Sum of vertical forces = 0
EXAMPLE — inclined plane:
Object on slope at angle θ:
Component of weight along slope: W sin θ (down the slope)
Component of weight perpendicular to slope: W cos θ (into slope)
Normal contact force = W cos θ
Friction force (if stationary) = W sin θ
⚠️ Common Mistake
All forces in a free body diagram act ON the object — not forces the object exerts on others. Weight always acts downward from the centre of mass. Normal contact force is PERPENDICULAR to the surface — not vertical (unless surface is horizontal).