UY1: Mechanics
University Physics Year 1 mechanics: kinematics, Newton’s laws, work-energy, momentum, centre of mass, and rotation.
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; linear momentum; 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.
- UY1: Basics & KinematicsModel motion with calculus-based kinematics in one and two dimensions, including projectiles and circular motion.
- UY1: Linear Momentum, Impulse & CollisionsApply the impulse–momentum theorem and momentum conservation to elastic and inelastic collisions.
- UY1: Resistive ForcesSolve linear and quadratic drag models for velocity against time and terminal speed.
- UY1: Uniform Circular Motion & Non-uniform Circular MotionResolve acceleration into radial and tangential parts for uniform and non-uniform circular motion.
- UY1: Concept of WorkFind the work done by constant and variable forces.
- UY1: Potential Energy & Conservative ForcesRelate conservative forces to potential-energy functions and use F = -dU/dx.
- UY1: Work-Energy TheoremDerive the work–energy theorem and use it to find speeds from the net work done.
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).
Further mechanics pages
These pages extend the lessons to variable mass, systems of particles and rotation.
Variable mass
- Rocket Propulsion — Variable mass systems.
Centre of mass
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What Is Centre of Mass? — Definition and calculation for discrete systems.
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Motion of System of Particles — Dynamics of the centre of mass.
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CM: Triangle — Calculating CM for a continuous right-angle triangle.
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CM: Cone — Calculating CM for a solid cone.
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Sample Questions — Practice problems for Centre of Mass.
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Pizza with a Hole — A compact centre-of-mass puzzle using subtraction of shapes.
Rotation and moment of inertia
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Rigid Body Rotation — Kinematics of rotation.
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Rotational Kinematics — Equations of motion for constant angular acceleration.
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Moment of Inertia — Rotational inertia and the parallel axis theorem.
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I: Rigid Rod — Derivation for a uniform rod.
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I: Cylinder — Derivation for solid and hollow cylinders.
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I: Solid Sphere — Derivation for a solid sphere.
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I: Spherical Shell — Derivation for a thin spherical shell.
Rotational dynamics
- Torque & Angular Acceleration — Newton’s 2nd Law for rotation.
- Rotational Work & Energy — Work, power, and kinetic energy in rotation.
- Rolling Motion — Rolling without slipping.
- Sphere on Incline — Dynamics of a rolling sphere on a ramp.
- Advanced Rolling — Friction, slipping, and complex rolling problems.
- Angular Momentum — Conservation of angular momentum.
Related A-Level and H3 topics
- Oscillations (A Level): Oscillations hub, Simple Harmonic Motion, SHM Graphs, Damping & Resonance
- Gravitation & orbits (A Level): Gravitation hub, Elliptical orbits, Escape speed, Gravitational potential
- Statics / rigid-body equilibrium (A Level): Torque & Couples, Centre of Gravity
- Frames & collisions (H3 enrichment): Inertial vs Non-inertial Frames, Collision problems in COM frame