What does the Mechanics option in OCR Further Maths A cover?

The optional Mechanics paper (Y543) covers work, energy and power (the work-energy principle, conservation of energy, power as force times velocity, Hooke's law for elastic strings and springs, and elastic potential energy), momentum and impulse (conservation of momentum, the impulse-momentum principle, the coefficient of restitution, and direct and oblique collisions), circular motion (angular speed, centripetal force, horizontal circles such as the conical pendulum and banked tracks, and vertical circles), and centre of mass (systems of particles, uniform laminas, composite bodies and suspension). It is one of the two optional papers a candidate may choose.

Which Mechanics topics carry the most marks in OCR Further Maths A?

Circular motion and the collision problems are the heaviest, because each is a multi-step structured question often combining several principles. Energy methods and centre of mass are reliable sources of marks. Fluency with the work-energy principle, conservation of momentum with the coefficient of restitution, and the centripetal force equation is the single biggest enabler in this option.

What techniques recur across the OCR Mechanics content?

Applying the work-energy principle and conservation of energy, using power equals force times velocity, using Hooke's law and the elastic potential energy formula, conserving momentum and applying the coefficient of restitution, resolving for the centripetal force in horizontal and vertical circles, combining energy conservation with the centripetal equation in a vertical circle, and finding a centre of mass by the mass-weighted average (treating composite parts as point masses). These are automatic by exam day.

What is the most common Mechanics mistake in OCR Further Maths A?

Treating the centripetal force as an extra force on the diagram, and sign errors in momentum and impulse. Other frequent errors are forgetting the work done against resistance in the work-energy principle, confusing extension with length in Hooke's law, assuming kinetic energy is conserved when the coefficient of restitution is less than one, and adding a removed piece instead of subtracting it in a centre-of-mass calculation. Always draw a clear diagram and fix a positive direction.

How should I revise the OCR Mechanics option?

Work topic by topic against the specification, drilling each technique until it is automatic, then practise mixed problems under timed conditions. Keep a sheet of standard results: the energy formulae, power equals force times velocity, Hooke's law and the elastic energy formula, conservation of momentum with the restitution definition, the centripetal force, and the centre-of-mass formula. Always draw a force diagram, fix a positive direction, and state what provides the centripetal force.

EnglandFurther Maths

OCR A-Level Further Maths A Mechanics option: work and energy, momentum, circular motion and centre of mass

A deep-dive OCR A-Level Further Mathematics A guide to the optional Mechanics paper (Y543): work, energy and power with elasticity, momentum, impulse and collisions, circular motion, and centre of mass, with the techniques OCR repeats in the Mechanics option.

Generated by Claude Opus 4.818 min readH245/Y543Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What the Mechanics option demands
Energy and momentum
Circular motion and centre of mass
How the Mechanics content is examined
Check your knowledge

What the Mechanics option demands

The Mechanics option of OCR A-Level Further Mathematics A (H245) is one of the four optional papers (Y543), of which a candidate chooses two. It develops mechanics beyond A-Level Mathematics, applying calculus and vectors to energy, momentum, circular motion and rigid bodies. The examiners reward a clear model (a labelled force diagram and a chosen positive direction), consistent units, and the correct principle for each situation.

This guide walks through the four Mechanics topics in a logical order, then sets out the exam patterns OCR repeats. Each topic has a matching dot-point page with worked exam questions; this overview ties them together.

Energy and momentum

Work, energy and power covers the work done by a force, kinetic and gravitational potential energy, the work-energy principle and conservation of energy, power as force times velocity, and Hooke's law and elastic potential energy for strings and springs. Momentum, impulse and collisions covers linear momentum and impulse, conservation of momentum, the coefficient of restitution from Newton's experimental law, and direct and oblique collisions, including impacts with a fixed surface.

Circular motion and centre of mass

Circular motion covers angular speed, the centripetal acceleration and force, horizontal circles (the conical pendulum and banked tracks) and vertical circles (with the conditions for a string to stay taut). Centre of mass covers the centre of mass of a system of particles, of a uniform lamina by symmetry or integration, and of a composite body, with applications to suspension.

How the Mechanics content is examined

A typical OCR profile for this option:

Energy questions. Use the work-energy principle or energy conservation, or an elastic string and its stored energy.
Collision questions. Conserve momentum and apply the coefficient of restitution, in one or two dimensions.
Circular motion questions. Find a tension or speed in a horizontal or vertical circle.
Centre of mass questions. Locate the centre of mass of a composite lamina, or find a suspension angle.

Check your knowledge

A mix of recall and technique questions covering the Mechanics content. Attempt them under timed conditions, then check against the solutions.

State the work-energy principle. (1 mark)
State the formula for power in terms of force and velocity. (1 mark)
State Hooke's law for an elastic string. (1 mark)
Define the coefficient of restitution. (1 mark)
State the magnitude of the centripetal force. (1 mark)
State the centre-of-mass coordinate formula for a system of particles. (1 mark)

Check your knowledge: further mechanics

Recall questions covering the key principles and formulas from the Mechanics option.

Step 1: State the work-energy principle

The work-energy principle links kinematics and forces: all the work done by every force acting on a body (including resistance) equals the resulting change in kinetic energy, not just work done by a single force.

Answer: The net work done on a body equals its change in kinetic energy.

Step 2: State the formula for power in terms of force and velocity

Power is the rate of doing work; when a constant force $F$ moves its point of application at velocity $v$ , work is done at rate $Fv$ .

Answer: $P = Fv$ (force times velocity).

Step 3: State Hooke's law for an elastic string

Hooke's law says the tension in an elastic string is proportional to its extension $x$ beyond the natural length $l$ ; the constant of proportionality is the modulus of elasticity $\lambda$ .

Answer: $T = \dfrac{\lambda x}{l}$ , with modulus $\lambda$ , natural length $l$ , extension $x$ .

Step 4: Define the coefficient of restitution

Newton's experimental law states that the ratio of the speed of separation to the speed of approach along the line of impact is constant for a given pair of surfaces; this constant $e$ satisfies $0 \le e \le 1$ .

Answer: $e = \dfrac{\text{speed of separation}}{\text{speed of approach}}$ , with $0 \le e \le 1$ .

Step 5: State the magnitude of the centripetal force

A body moving in a circle of radius $r$ at speed $v$ (or angular speed $\omega$ ) requires a net inward force to maintain the circular path; this is provided by existing forces such as tension, normal reaction or gravity, not by a separate centripetal force.

Answer: $\dfrac{mv^2}{r} = mr\omega^2$ , directed towards the centre.

Step 6: State the centre-of-mass coordinate formula for a system of particles

The centre of mass is the mass-weighted average position of the system; each particle's position is weighted by its mass and the total is divided by the total mass.

Answer: $\bar{x} = \dfrac{\sum m_i x_i}{\sum m_i}$ (and similarly for $\bar{y}$ ).

Sources & how we know this

OCR A Level Further Mathematics A (H245) specification — OCR (2017)