Unit 2 · Topic 06

Free-body diagrams

A free-body diagram translates a physical situation into a vector inventory of forces acting on an isolated system.

Unit 2FBDsOpen navigation

Concept 01

Isolate the system

Essential The minimum you should retain

First choose and isolate the system. Then draw only forces exerted on it by the surroundings.

UnderstandInterpret and connect

The boundary must be unambiguous: a box, a person, or a collection of bodies can be different systems in the same scene.

DeepenFormulation and conditions

Isolating the system turns each relevant external interaction into a force vector applied to the particle or body model.

ExploreConnections for further study

Comparing different boundaries helps decide which internal forces can be omitted without losing the physical question.

An isolated box has three arrows: support upward, weight downward, and a push to the right.boxsupportweighthand on box

The FBD contains the upward support force, downward weight, and the hand's force toward +x. It contains neither velocity, ma, nor the reaction on the hand.

Concept 02

Force inventory

Essential The minimum you should retain

For every arrow ask: who exerts it, which system receives it, what interaction it represents, and which way it points.

UnderstandInterpret and connect

Velocity, acceleration, trajectory, ma, and a supposed force of motion are not forces. A force exerted by the system on another body also does not belong.

DeepenFormulation and conditions

A complete inventory comes from examining interactions that cross the boundary, not memorizing a set of typical arrows.

ExploreConnections for further study

An incorrect FBD often reveals an ambiguous boundary before an algebra error; fix the model before calculating.

An isolated box has three arrows: support upward, weight downward, and a push to the right.boxsupportweighthand on box

The FBD contains the upward support force, downward weight, and the hand's force toward +x. It contains neither velocity, ma, nor the reaction on the hand.

Concept 03

Axes and components

Essential The minimum you should retain

Choose axes after understanding the situation. A force can be decomposed into components that help with addition.

UnderstandInterpret and connect

Components inherit signs from the axes. Drawing them as aids does not create extra forces.

DeepenFormulation and conditions

Projecting every force onto a basis produces scalar equations equivalent to the original vector sum.

ExploreConnections for further study

Axes aligned with acceleration or a dominant geometry can reduce unknowns without changing the physics.

A diagonal force from the origin is decomposed into horizontal and vertical components.FFₓFᵧ

Fₓ and Fᵧ are projections of the same force F onto the chosen axes. The dotted guides show decomposition without adding interactions.

Concept 04

From an FBD to acceleration

Essential The minimum you should retain

The reading flow is FBD → net force → Newton equation → acceleration.

UnderstandInterpret and connect

A physical diagram shows the scene; an FBD shows forces on a system; a kinematic diagram shows position, velocity, or acceleration.

DeepenFormulation and conditions

After summing arrows by components, ΣF→ext=ma→ \sum\vec F_{ext}=m\vec a links the interaction representation with the change in motion.

ExploreConnections for further study

Reconstructing a situation from an FBD requires recognizing what information was lost by isolation and which assumptions remain implicit.

An isolated box has three arrows: support upward, weight downward, and a push to the right.boxsupportweighthand on box

The FBD contains the upward support force, downward weight, and the hand's force toward +x. It contains neither velocity, ma, nor the reaction on the hand.

Two opposite force vectors produce a resultant of four newtons to the right.7 N3 NΣF = 4 N

The 7 N and 3 N forces act on the same system in opposite directions. Their sum is 4 N toward +x; the resultant is shown as a calculation, not a third interaction.

Concept review

Common errors

Each warning includes a concrete way to review the reasoning, not only an incorrect-answer marker.

Including velocity as a force arrow.

An FBD contains interactions on the system; show velocity in a separate kinematic diagram.

Adding ma as though it were a force.

ma is the dynamical result of the sum, not another interaction.

Adding the force exerted by the system on another body.

Draw only forces that act on the isolated system.

Counting a force and its components as simultaneous forces.

Use the original vector or its components for addition, but not both inventories.