Choose a situation
Use the home screen to choose the physical setup you want to model. The top-left ΣF icon always brings you back here.
This site is designed to make the modelling decisions in 9MA0 visible. Start with a physical situation, decide what forces belong in the model, then turn the force diagram into mathematics.
You do not need to use every control. A useful first visit follows this sequence.
Use the home screen to choose the physical setup you want to model. The top-left ΣF icon always brings you back here.
Select Explore, Build, or Practice. The same mechanics engine is underneath all three; the amount of support changes.
Look at the objects, geometry, contacts and motion information first. The physical picture deliberately does not contain force arrows.
Focus on one body at a time. Predict the forces, reveal the free-body diagram, and click a force to see why it acts and where its partner acts.
Choose useful axes, resolve only when needed, then move through the Mathematics steps from modelling to a checked result.
Explain what the answer means physically. Change one variable and predict what should change before you move it.
You choose a mode immediately after choosing a situation. You can switch mode later from the top of the page.
The modelling layers are available immediately. Change one variable at a time, predict what will happen, then inspect the force diagrams and Mathematics workspace.
Start from the physical picture and choose which types of force you expect. Reveal the generated FBD only after committing to a prediction.
Read the question and physical model, then work on paper. Reveal the correct diagrams or full solution only when you want feedback.
The site separates the real situation from the mathematical representations built from it.
This shows objects, strings, surfaces, hinges, geometry and motion information. It does not show force arrows. Ask: what is touching or pulling what?
This shows only the forces acting on the selected body. Weight acts through the centre of mass; contact forces act at contacts; tension acts along a string.
When you choose components, the original oblique force is replaced by its components. You never see the original force and its components as if they were three separate forces.
Keep the FBD clean with Symbols only. Use On hover / tap to inspect one value, or Value key below to see the current values without lengthening every arrow label.
A system diagram appears only when grouping bodies is useful. Internal forces such as contact or tension can disappear from a whole-system equation because the interaction is inside the chosen boundary.
Click a force arrow to see its explanation. Newton III partners are linked across diagrams. Equal tensions in an ideal string are shown as a constraint, not incorrectly labelled as a Newton III pair.
Essential shows the angles needed immediately. More detail reveals useful equal, complementary or perpendicular angles when the geometry is part of the modelling.
The assumption chips tell you what the mathematical model is ignoring or idealising. Open the explanation and ask which conclusion depends on each assumption.
These examples show the thinking the site is trying to develop, not just which buttons to press.
Goal: understand friction and resolving weight.
Goal: connect two FBDs without confusing equal tension with Newton III.
Goal: see why force positions and pivot choice matter.
The most useful exam routine is to delay the reveal until you have committed something to paper.
A quick-reference guide for deciding what belongs on a mechanics model, where forces act, and what common modelling words actually change.
Ask what is interacting with the body. Every force should have a physical reason.
Cause: gravitational interaction with Earth.
Direction: vertically downward.
Where: centre of mass; for a uniform rod, the midpoint.
Cause: contact between surfaces.
Direction: perpendicular to the contact surface.
Where: at the contact.
At a rough contact: the surface may exert both normal reaction R and friction F.
Resultant: these can be represented by one total contact reaction.
Magnitude: C=√(R²+F²) when the components are perpendicular.
Cause: rough contact.
Direction: opposes relative motion or the tendency to slide.
Where: along the contact surface.
Cause: a taut string or cable pulling on a body.
Direction: along the string, away from the body.
Where: at the attachment point.
Cause: a rod or member pushing on a joint/body.
Direction: along the member.
Where: at the joint or attachment.
Cause: an external push or pull.
Direction: as specified in the problem.
Where: at the stated application point.
Cause: the surrounding medium or a stated resistance to motion.
Direction: opposite the motion relative to the medium.
Where: usually represented as a single force in a particle model.
Cause: a pin, hinge, support or axle constraining the body.
Direction: not always known in advance; often resolve into horizontal and vertical components.
Where: at the hinge/support.
Mechanics questions often test the decision about which law applies before they test the algebra.
If the resultant force on a particle is zero, its acceleration is zero. It may be stationary or moving with constant velocity.
A common mistake is to conclude that zero resultant means the object must be at rest.
The vector resultant determines the acceleration. Resolve in useful directions or use vector notation.
The acceleration points in the direction of the resultant force, not necessarily the direction of the velocity.
Two interacting bodies exert equal-magnitude, opposite-direction forces on each other. The pair acts on different bodies.
Equal tensions on two particles are not automatically a Newton III pair.
These words are instructions about what to include or ignore. For each one, ask: what complexity does this remove, and what equation or force relationship does it justify?
Size, shape and rotation are ignored. Forces can be represented through one point when only translation matters.
The object does not deform. Force positions matter, so moments can be taken about points.
Mass is evenly distributed, so its centre of mass is at the midpoint.
Its own mass is neglected, simplifying the force model. In 9MA0, “light” is normally used for connectors/supporting components such as strings, rods or pulleys—not as a synonym for “ignore the weight of a massive particle”.
The total string length is fixed. Connected particles have linked displacement, velocity and acceleration magnitudes while the string is taut.
The string remains straight and can transmit tension. If it becomes slack, tension becomes zero and the motion constraint disappears.
No friction acts at that contact. A normal reaction may still act.
Friction may act. Its magnitude depends on whether the contact is static, limiting or sliding.
The pulley does not introduce a frictional difference in tension between the two sides of the same ideal string.
No friction acts at the contact. The contact reaction acts normal to the touching surfaces; for a rod resting on a smooth peg, this is perpendicular to the rod.
The body is on the point of slipping, so the friction has reached its maximum value: F=μR.
No drag force is included. This is common unless resistance is explicitly given.
Use one fixed gravitational field strength throughout the model. 9MA0 normally uses g=9.8 m s⁻², but a question may specify another value such as 10 m s⁻²; the lab's Advanced settings allow this to be changed.
Each example follows the same question: “What is interacting with the body?”
mg sin θ and mg cos θ are components of the one weight force.
They can be equal because of the light-string/smooth-pulley model.
Static friction takes the value needed up to its maximum.
A body can be moving one way while accelerating the other way.
Tension/contact can disappear from a whole-system equation when both interacting bodies are included.
Do not move support forces to the centre of a rigid body just to make the picture simpler.
Newton I says zero resultant gives zero acceleration; a body may still move with constant velocity.
At a rough contact, normal reaction and friction are perpendicular components of the resultant contact force.