First-year university mechanics
Study first-year university mechanics, from kinematics and Newton’s laws to work and energy, momentum, centre of mass and rotation.
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Before you begin
UY1 mechanics builds from kinematics and forces to energy and momentum methods. Choose your method early: forces, energy or momentum.
Be comfortable with: A-Level kinematics; circular motion; work, energy and power; momentum conservation; and vectors and calculus from mathematics for undergraduate physics.
Learning goals
- Formulate motion and force models with explicit coordinates, assumptions, and units.
- Apply work–energy and momentum methods, then interpret the physical result.
- Analyse centre-of-mass and rotational dynamics using torque, inertia, energy, and angular momentum.
Lessons
Work through them in order.
- Mechanics foundations and kinematicsModel motion with calculus-based kinematics in one and two dimensions, including projectiles and circular motion.
- Momentum, impulse and collisionsApply the impulse–momentum theorem and momentum conservation to elastic and inelastic collisions.
- Resistive forcesSolve linear and quadratic drag models for velocity against time and terminal speed.
- Uniform and non-uniform circular motionResolve acceleration into radial and tangential parts for uniform and non-uniform circular motion.
- Work done by a forceFind the work done by constant and variable forces.
- Potential energy and conservative forcesRelate conservative forces to potential-energy functions and use F = -dU/dx.
- The work–energy theoremDerive the work–energy theorem and use it to find speeds from the net work done.
- Kinematics of angular motionUse signed angular quantities, constant-acceleration equations and graph areas to describe rotation.From GCE A-Level H3 Physics
- Moment of inertiaExplain how the chosen axis and squared perpendicular distances determine moment of inertia.From GCE A-Level H3 Physics
- Dynamics of angular motionCalculate signed external torques and angular acceleration about a fixed axis.From GCE A-Level H3 Physics
- Torque and angular momentumFind point-mass and rigid-body angular momentum and apply external torque and conservation about a stated axis.From GCE A-Level H3 Physics
- Rotational kinetic energyDerive rotational kinetic energy, distinguish it from total energy and combine it with COM translation.From GCE A-Level H3 Physics
- Rolling motion: energy and frictionCombine translational and rotational energy, derive rolling acceleration and test the required friction.From GCE A-Level H3 Physics
- Calculating moments of inertiaChoose a differential mass element, integrate over a uniform body and shift to a parallel axis through the correct centre of mass.From GCE A-Level H3 Physics
Practise and check
Topic reference
Choosing a method
Mechanics problems usually simplify if you pick the right “engine” early:
- Newton + FBD: when you need forces/accelerations or time dependence (e.g. drag) → start with a free-body diagram and ∑ vector F = m vector a.
- Work-energy: when you need a speed after moving through a distance, especially with conservative forces → Wₙₑₜ = Δ K and/or K + U bookkeeping.
- Momentum/impulse: when forces are brief/large or internal forces dominate (collisions, explosions, recoil) → conserve vector P if external impulse is negligible.
- CM (systems): when many bodies interact internally → track the centre of mass with ∑ vector Fₑₓₜ = M vector a_CM (Motion of system of particles).