Pearson International A Level Further Mathematics: M2 Mechanics 2
Pearson International A Level Further Mathematics notes on two-dimensional kinematics, centres of mass, work, energy, collisions and rigid bodies.
M2 is an externally assessed modular unit used within Pearson Edexcel International A Level Further Mathematics. The current Mathematics, Further Mathematics and Pure Mathematics specification is Issue 3. This note follows the official M2 order and keeps qualification cash-in choices separate from the mathematical content: your centre must still confirm that the unit combination is eligible for the award you intend to claim.
Official unit scope
- Kinematics of a particle moving in a plane.
- Centres of mass of discrete and composite bodies.
- Work, energy and power.
- Impulse, momentum and direct collisions.
- Further Newtonian modelling.
The specification assumes prerequisite knowledge stated for the unit, so later-unit questions may combine earlier methods without re-teaching them. Treat the list above as an integrated toolkit. A question can begin in one topic and finish in another, such as using algebra to form a model, calculus to optimise it and a graph to interpret the result.
Core reasoning and methods
- Resolve plane motion into perpendicular components that share the same time.
- For composite centres of mass, treat removed pieces as negative mass only after defining a common origin.
- Use momentum conservation for an isolated collision and add restitution only along the line of impact.
Write mathematical arguments so another reader can reproduce every transition. Define symbols that are introduced, preserve exact values until a decimal is requested, and place restrictions beside the step that creates them. Calculator use can support arithmetic, graph exploration and checking, but it does not replace a proof, derivation or required chain of working.
When a model is used, state the simplifying assumptions and interpret the answer in the original setting. A mathematically valid root may be inadmissible because it lies outside a time interval, represents a negative length, violates a probability range or conflicts with a geometric domain. The final check is therefore both algebraic and contextual.
Worked example
A 2 kg particle moving at 6 m/s collides directly with a 1 kg particle at rest and they coalesce. Conservation of momentum gives 2(6) + 1(0) = 3v, so v = 4 m/s in the original direction. Initial kinetic energy is 36 J and final kinetic energy is 24 J, so 12 J is transformed to other forms. Momentum is conserved because the external impulse is neglected; kinetic energy is not conserved in a perfectly inelastic collision. Stating both principles avoids the common error of assuming that every collision conserves kinetic energy.
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