A-level Maths Mechanics → Further Mechanics 1
Further Mechanics 1 assumes the vectors, kinematics and Newton's-law modelling from A-level Maths are fluent. It then introduces five new mechanics areas centred on impacts and energy. The algebra is not the main difficulty: the jump is choosing the right conservation principle, keeping directions consistent and knowing what changes during a collision.
The biggest jumps
- Momentum and impulse are new quantities, conservation of momentum becomes a central tool, and direction matters from the start.
- Work, energy and power provide a second route through problems that A-level Maths handles with forces and acceleration.
- The coefficient of restitution drives both direct and oblique collision models.
Momentum and impulse
You can already
Model velocity and acceleration as vectors and apply Newton's laws to particles.
Now you'll
Define momentum and impulse, use the impulse–momentum principle in scalar and vector form, and conserve momentum when two spheres collide directly.
Work, energy and power
You can already
Resolve forces and use to model motion and equilibrium.
Now you'll
Calculate work, kinetic and potential energy and power, then use the work–energy principle and conservation of mechanical energy.
Elastic strings and springs
You can already
Model connected particles, tensions and equilibrium using Newton's laws.
Now you'll
Model elastic strings and springs with Hooke's law and calculate the elastic energy they store.
Elastic collisions in one dimension
You can already
Model straight-line particle motion and keep a consistent positive direction.
Now you'll
Use Newton's law of restitution for direct impacts, calculate kinetic-energy loss, and handle successive impacts between spheres or with a smooth plane.
Elastic collisions in two dimensions
You can already
Resolve vectors into perpendicular components and model motion in a plane.
Now you'll
Extend restitution to oblique impacts between smooth spheres or with a fixed surface, including kinetic-energy loss and successive impacts with smooth planes.
Bridge the gap before term starts
A few sessions over the summer on exactly these new topics is the difference between catching up and getting ahead. Your first lesson is free.