Free Body Diagrams | Physics

📖 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).

📐 Key Equations

Horizontal component: Fx = F cos θ

Vertical component: Fy = F sin θ

📌 Key Note

FBD: all forces on one object as arrows (length = magnitude). Balanced: resultant = 0, object stationary or constant velocity. Unbalanced: net force → acceleration. Resolve angled forces: Fx = F cosθ, Fy = F sinθ. Equilibrium: sum horizontal = 0 AND sum vertical = 0.

🎯 Matching Activity — Free Body Diagrams

Match each situation to the correct FBD description. — drag the symbols on the right to match the component names on the left.

Book at rest on table

Drop here

Skydiver at terminal velocity

Drop here

Car accelerating

Drop here

Object on slope at rest

Drop here

Weight down = drag up — balanced, constant velocity

Normal force perpendicular to slope = W cosθ; friction along slope = W sinθ

Weight down = normal contact up — balanced forces, resultant = 0

Thrust > drag — net forward force, accelerates in direction of motion

⭐ Higher Tier Only

HT only — draw and interpret free body diagrams. Resolve forces into perpendicular components. Determine resultant force from FBD using scale drawing or components. Identify whether an object is in equilibrium from a FBD.

🔬 Triple Science Only

Free body diagrams as a separate topic (HT only) — part of the physics-only extended forces content.

🎯 Test Yourself

Question 1 of 2

1. A 10 N force acts at 30° to the horizontal. What is the vertical component?

2. In a free body diagram of a skydiver falling at terminal velocity, what must be true?

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⚡ Free Body Diagrams

What Is a Free Body Diagram?

Interpreting Free Body Diagrams

Resolving Forces from Free Body Diagrams

Mr. Badmus AI