Knowledge organisers

Mechanics 1 (M1): Edexcel IAL Maths knowledge organiser

Everything to know about mechanics 1 (m1) on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Particle: A body treated as a point: its size is ignored.
Momentum: Mass × velocity; it is conserved in a collision when no outside force acts.
Impulse: Change in momentum: I = mv − mu = Ft.
Limiting friction: The greatest friction possible, F = μR, when sliding is about to start.

Key formulas

suvat	\(v=u+at,\) \(s=ut+\tfrac12at^2,\) \(s=vt-\tfrac12at^2,\) \(s=\tfrac12(u+v)t,\) \(v^2=u^2+2as\)
Vectors	\(\mathbf v=\mathbf u+\mathbf at,\) \(\mathbf r=\mathbf r_0+\mathbf vt,\) \(\text{speed}=\|\mathbf v\|\)
Newton's 2nd law; weight	\(F=ma,\) \(W=mg\ (g=9.8\text{ m s}^{-2})\)
Friction	\(F\le\mu R;\) \(\text{limiting }F=\mu R\)
Momentum; impulse	\(p=mv;\) \(I=Ft=mv-mu\)
Conservation of momentum	\(m_1u_1+m_2u_2=m_1v_1+m_2v_2\)
Moments	\(\text{moment}=F\times d_\perp;\) \(\text{equilibrium: }\textstyle\sum F=0,\ \sum M=0\)
Slope at \(\theta\): weight component \(mg\sin\theta\) down the slope; \(R=mg\cos\theta\) if nothing else acts perpendicular to it
Velocity–time graph: gradient = acceleration, area = displacement

Worked example

A particle of mass 2 kg moving at 3 m s⁻¹ hits a particle of mass 1 kg at rest. They join together. Find their common speed.

Momentum before = 2 × 3 + 1 × 0 = 6
Momentum after = (2 + 1)v

Answer: v = 2 m s⁻¹

Common mistakes

Too many significant figures after using g = 9.8
Momentum: directions and signs
Area under a v–t graph read as acceleration
Sign convention changed mid-question

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Describe how mechanics models are built and refined, and state assumptions such as modelling an object as a particle or a rope as light and inextensible.
Distinguish distance from displacement and speed from velocity, and use travel graphs to find total distance travelled when motion changes direction.
Apply Newton's second law F = ma to particles moving in a straight line under several forces, finding accelerations, forces and masses.
Calculate momentum and impulse, and use impulse = change in momentum to find velocities or forces in one-dimensional problems.
Solve equilibrium problems with limiting friction, finding the least or greatest force needed to keep a particle at rest on a rough surface.
Solve problems where a rod is on the point of tilting about a support, using the fact that the other reaction is zero.

The printable sheet

Mechanics 1 (M1) knowledge organiser for Edexcel IAL Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Mechanics 1 (M1) knowledge organiser (Edexcel IAL Maths), A4. Download the PDF.

Revise it next

Other Edexcel IAL Maths topics: Pure Mathematics 1 (P1) · Pure Mathematics 2 (P2) · Pure Mathematics 3 (P3) · Pure Mathematics 4 (P4) · Statistics 1 (S1) · All Edexcel IAL Maths organisers