What rigid body mechanics content do IB Physics HL students need to know?

Students should understand angular displacement, angular velocity, angular acceleration, torque, moment of inertia, rotational kinetic energy and angular momentum. They must connect these ideas through relationships such as τnet = Iα, Ek,rot = ½Iω² and L = Iω in appropriate situations. Rolling motion requires the link v = ωR and usually involves both translational and rotational kinetic energy. Students should also be able to apply rotational equilibrium and conservation of angular momentum. Formula use must be supported by force diagrams, axis choices and clearly stated physical assumptions.

How is rigid body mechanics examined in IB Physics HL?

Rigid body mechanics can appear in Paper 1A multiple-choice questions, Paper 1B data-based questions, and Paper 2 short-answer or extended-response questions. Paper 1A may test rapid recognition of torque directions, units or moment-of-inertia effects. Paper 1B can place rotational ideas in an experimental or graphical context. Paper 2 may require a linked calculation involving torque, angular acceleration, energy or angular momentum. The IB does not publish a guaranteed number of rigid body mechanics marks for each examination paper.

When should I use conservation of angular momentum?

Use conservation of angular momentum when the net external torque about the chosen axis is zero or negligible during the relevant interval. You should state this condition explicitly rather than writing Iiωi = Ifωf without justification. Internal forces can alter the distribution of mass and therefore change the moment of inertia, but they do not change total angular momentum in an isolated system. Rotational kinetic energy may change if internal forces perform work. Collisions involving rotation therefore require careful separation of angular momentum conservation from energy conservation.

How do I choose the best axis for calculating torque?

Choose an axis that simplifies the torque equation and matches the motion being considered. In equilibrium problems, an axis through an unknown support force is often effective because that force then has zero moment arm. For an object rotating around a fixed axle, the physical rotation axis is normally the natural choice. Every torque must be calculated about the same axis within a single equation. If you change axes, both the torque calculations and the relevant moment of inertia may change.

Why do I keep getting the wrong answer in rolling-motion questions?

The most common cause is treating the object as a particle and including only ½Mv² as its kinetic energy. A rolling rigid body also has rotational kinetic energy ½Iω². For rolling without slipping, the variables are connected by v = ωR, so they are not independent. The moment of inertia must correspond to the correct shape and axis. You should also examine whether static friction supplies the torque needed to produce rotation rather than automatically assuming friction is absent.

What is the best way to practise IB rigid body mechanics questions?

Attempt complete questions without looking at the solution, then compare every step with a worked video solution. This exposes errors in modelling, axis selection and torque signs that passive note-reading rarely reveals. Group questions by recurring format, such as equilibrium, rolling, angular acceleration and angular momentum. Record each mistake by its underlying cause and repeat a similar question soon afterward. Once individual methods are secure, complete mixed and timed sets so that you must identify the correct approach without being told the topic.

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IB Physics Rigid Body Mechanics (HL) Questions Guide

• 30 Jul 2026•11

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IB Physics Rigid Body Mechanics (HL) Questions Guide

• 30 Jul 2026•11

IB Physics rigid body mechanics (HL) questions become much more manageable when you classify the motion, draw the forces, choose a rotation axis, and apply the appropriate rotational law. The same structures recur: torque and angular acceleration, rotational energy, rolling without slipping, angular momentum, and equilibrium.

Under the current IB Physics course, first assessed in 2025, A.4 Rigid body mechanics is an HL-only part of the Space, time and motion theme. It can be examined through Paper 1A multiple-choice questions, Paper 1B data-based questions, and Paper 2 short-answer or extended-response questions, although the IB does not guarantee a fixed number of A.4 marks on each paper.

What rigid body mechanics questions test

A rigid body is an idealized object whose shape and dimensions do not change as forces act on it. Unlike a particle, it can rotate, so its response depends not only on the resultant force but also on where each force is applied.

The central ideas are closely related to familiar linear mechanics:

Linear mechanics	Rotational mechanics
Displacement `s`	Angular displacement `θ`
Velocity `v`	Angular velocity `ω`
Acceleration `a`	Angular acceleration `α`
Mass `m`	Moment of inertia `I`
Force `F`	Torque `τ`
Momentum `p = mv`	Angular momentum `L = Iω`
`F = ma`	`τnet = Iα`
`Ek = ½mv²`	`Ek,rot = ½Iω²`

This analogy is useful, but it is not merely a list to memorize. Moment of inertia depends on how mass is distributed relative to the chosen axis, so two objects with the same mass can respond differently to the same torque.

A reliable method for answering questions

1. Identify the physical situation

Decide whether the object is:

rotating about a fixed axis;
translating and rotating simultaneously;
rolling without slipping;
in rotational equilibrium; or
isolated sufficiently for angular momentum to be conserved.

Do not select an equation only because its variables appear in the question. First identify the governing principle.

2. Draw forces and select an axis

Mark every external force, including weight, normal reaction, tension, friction and applied forces. Then choose the axis about which torques will be calculated.

A useful axis often passes through an unknown support force. Because that force then has zero perpendicular distance from the axis, it produces no torque and disappears from the torque equation.

3. Assign a torque sign convention

State that anticlockwise torques are positive and clockwise torques are negative, or use the opposite convention consistently. Calculate net torque, not the magnitude of one convenient torque.

For a force applied at position vector r, use:

τ = rF sin φ

Here φ is the angle between the radius vector and the force, not automatically the angle shown most prominently in the diagram. Equivalently, torque is force multiplied by the perpendicular distance from the axis to the force's line of action.

4. Connect the torque to the motion

For rotation about a fixed axis:

τnet = Iα

If angular acceleration is constant, rotational kinematics can then be used, such as ω = ω₀ + αt or ω² = ω₀² + 2αθ. Angular quantities should be expressed in radians when substituted into these relationships.

5. Check units and physical meaning

Torque is measured in N m, while energy is measured in joules. Although these units have the same base dimensions, torque should not normally be written in joules because the quantities represent different physical ideas.

Also test whether the result is sensible. A larger moment of inertia should produce a smaller angular acceleration for the same net torque.

Worked example: torque and angular acceleration

A uniform solid disc has mass 2.0 kg and radius 0.40 m. A tangential force of 3.0 N acts at its rim, and resistive torque is negligible.

For a uniform solid disc:

I = ½MR² = ½(2.0)(0.40)² = 0.16 kg m²

Because the force is tangential, it is perpendicular to the radius:

τ = rF = (0.40)(3.0) = 1.2 N m

Therefore:

α = τ/I = 1.2/0.16 = 7.5 rad s⁻²

If the disc starts from rest, its angular velocity after 2.0 s is:

ω = ω₀ + αt = 0 + (7.5)(2.0) = 15 rad s⁻¹

A strong solution shows the moment of inertia, torque and rotational dynamics steps separately. Jumping directly from force to angular acceleration often conceals an incorrect radius or inertia expression.

Recurring IB question formats

Rotational equilibrium

For an object in complete static equilibrium, both conditions are required:

ΣF = 0, for translational equilibrium;
Στ = 0, for rotational equilibrium.

A beam can have zero resultant force but still rotate if the forces form a couple. Conversely, zero net torque does not prove that the resultant force is zero.

Rolling without slipping

For pure rolling, the centre-of-mass speed and angular speed satisfy:

v = ωR

The total kinetic energy is:

Ek = ½Mv² + ½Iω²

A common mistake is to include only translational kinetic energy. On an incline, static friction may provide the torque needed for rotation even though it does no energy transfer at the instantaneous point of contact in the ideal no-slip model.

Conservation of angular momentum

Angular momentum is conserved only when the net external torque about the selected axis is zero. For a rigid body rotating about a fixed principal axis, L = Iω, giving:

Iiωi = Ifωf

If mass moves closer to the axis, the moment of inertia decreases and angular speed increases. Rotational kinetic energy is not necessarily conserved because internal work may change it.

Data-based and unfamiliar-context questions

Paper 1B or Paper 2 may provide graphs, experimental measurements or an unfamiliar rotating system. Extract the gradient or area only after identifying what it represents physically. For example, the gradient of an ω against t graph is angular acceleration, while the area under the graph is angular displacement.

Common pitfalls and how to avoid them

Using the full radius when a perpendicular distance is needed: Draw the force's line of action and mark the shortest distance to the axis.
Ignoring opposing torques: Write a signed torque sum before substituting values.
Using the wrong moment of inertia: Check both the object's shape and the specified axis.
Conserving angular momentum without justification: Explicitly state that net external torque is zero or negligible.
Forgetting rotational kinetic energy: A rolling object normally has both translational and rotational energy.
Mixing revolutions and radians: Convert revolutions using 1 revolution = 2π radians.
Assuming zero friction in rolling problems: Determine whether static friction is required to produce angular acceleration.
Rounding too early: Retain unrounded intermediate values and round the final answer appropriately.

How to revise rigid body mechanics efficiently

Re-reading notes can clarify definitions, but it does not build the sequence of decisions required under exam conditions. The fastest practical method is to attempt a question independently, commit to a complete solution, and then watch the method worked through line by line.

Use the A.4 rigid body mechanics questionbank and worked solutions to practise one recurring format at a time. Per-question video solutions are especially useful because they reveal where the axis was chosen, why a torque received a particular sign, and which conservation law was justified.

Keep an error log organized by cause rather than question number. Categories such as “wrong axis,” “missed rotational energy,” and “unjustified conservation” make patterns visible. The broader IB Physics Questionbank, A.4.2 moment of inertia resources, IB Physics course resources, and Physics data booklet resource can then be used to repair specific weaknesses.

Conclusion

Successful answers to IB Physics rigid body mechanics (HL) questions begin with a physical model, not an equation search. Identify the type of motion, draw the forces, choose an effective axis, calculate signed net torque, and justify any conservation principle before doing the algebra.

RevisionDojo can support this process with targeted question practice and worked explanations. Attempting A.4 questions before reviewing the per-question video solutions is the most useful next step because it develops both the mechanics and the exam method.

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