PHYS2250 Introductory Mechanics
The Complete Exam Bible · First Semester, 2026-27PHYS2250 Overview
- The University of Hong Kong
- First Semester, 2026-27
- Level 2 undergraduate
- Physics
- Two-hour written final
What the course is asking you to do
Introductory Mechanics is a mathematical course about building models from geometry and physical law.
- Assessment A written final, mid-term test, laboratory work and assignments make up the published total.
- Main method Represent the system before selecting an equation or conservation law.
- Permitted aid One double-sided A4 note sheet is allowed in both written tests.
- Best preparation Rebuild the problem-set methods on fresh numbers and geometries.
How PHYS2250 is assessed
| Component | Weight | Format |
|---|---|---|
| Final written examination | 50% | Two-hour written examination |
| Mid-term test | 25% | Two-hour test; current notice covers Chapters 1 to 8 |
| Laboratory works | 15% | Two required in-person laboratory sessions |
| Assignments | 10% | Four homework submissions |
The published teaching notes list these four shares and they sum to 100%. The current important-dates sheet describes the quiz share as a two-hour mid-term test. No hurdle status is asserted here. Confirm the final schedule and any operational changes on Moodle.
Current PHYS2250 dates
| Date | Item | Control |
|---|---|---|
| 21 September 2026 | Homework 1 | Due at 11:59 pm. |
| 19 October 2026 | Homework 2 | Due at 11:59 pm. |
| 30 October 2026 | Mid-term test | The current sheet states two hours and coverage through Chapter 8. |
| 9 November 2026 | Homework 3 | Due at 11:59 pm. |
| 30 November 2026 | Homework 4 | Due at 11:59 pm. |
Dates are as published in the current Moodle important-dates sheet and homework submission pages. Confirm exact deadlines and submission settings in the live LMS.
What PHYS2250 covers
Twelve chapters move from vectors and particle motion through force, momentum and rotation to energy, gravitation, oscillations and waves.
Dimensions and Vector Reasoning
dimensional checks, components, unit vectors and physical interpretationBuild the language before the model
Dimensional analysis rejects impossible relations before algebra, while vector resolution turns geometry into scalar equations.
- base dimensions and SI units
- dimensional consistency
- vector components
- dot and cross products
- physical sign interpretation
Kinematics and Projectile Motion
derivatives, motion graphs, constant acceleration and two-dimensional trajectoriesTranslate among equations, graphs and trajectories
Kinematics connects position, velocity and acceleration through derivatives and integrals.
- position velocity acceleration
- motion graph slopes
- constant acceleration
- projectile components
- inclined landing constraints
Newtonian Dynamics and Constraints
free-body diagrams, reference frames, strings, pulleys and contactIsolate the body before writing force equations
Newtonian dynamics starts by drawing only external forces on one selected body.
- Free-body diagrams
- Newton Laws
- Reference Frames
- String Constraints
- Contact and Separation
Circular Motion and Non-inertial Frames
radial acceleration, friction, banking and rotating observersSeparate turning from speeding up
Curved motion has radial acceleration that changes direction and tangential acceleration that changes speed. Real forces must supply the inward resultant.
- radial acceleration
- tangential acceleration
- static and kinetic friction
- banked motion
- rotating frames
Impulse, Momentum and Collisions
system boundaries, force-time impulse, restitution and variable massLet the system boundary decide what is conserved
Momentum methods depend on a declared system and the external impulse crossing its boundary.
- linear momentum
- force-time impulse
- collision conservation
- coefficient of restitution
- variable mass flux
Systems of Particles and Centre of Mass
weighted position, continuous distributions and centre-of-mass motionCompress internal complexity without losing mass distribution
The centre of mass is a mass-weighted position whose translation responds only to external force.
- weighted position
- continuous distributions
- symmetry arguments
- centre-of-mass motion
- internal and external forces
Rotational Kinematics and Dynamics
angular variables, torque, moment of inertia and equilibriumName the rotation axis before calculating
Angular kinematics relates angle, angular speed and angular acceleration, while torque depends on a perpendicular lever arm and moment of inertia depends on mass distribution.
- angular variables
- torque and lever arm
- moment of inertia
- parallel-axis theorem
- rigid-body equilibrium
Angular Momentum and Rolling Motion
angular impulse, conservation, rigid-body impact and no-slip rollingUse the origin and no-slip condition deliberately
Angular momentum is measured about a chosen origin, allowing an impact calculation to ignore an impulse whose line passes through that origin.
- particle angular momentum
- angular impulse
- conservation about an origin
- pure rolling
- translation and rotation energy
Work, Energy and Conservative Systems
line integrals, energy curves, power and nonconservative transfersUse states for endpoints and forces for local detail
Work integrates force along displacement, and the work-energy theorem remains valid for variable forces. Conservative forces permit potential energy and path-independent endpoint work.
- line-integral work
- work-energy theorem
- conservative forces
- potential-energy curves
- power and dissipation
Gravitation and Orbital Motion
inverse-square fields, shell results, circular orbits and escapeCombine central force with an energy reference
Newtonian gravitation is an inverse-square central force with negative potential when zero is chosen at infinity.
- inverse-square gravity
- field and potential
- spherical shell results
- circular orbits
- escape energy
Oscillations, Damping and Resonance
simple harmonic motion, characteristic roots, driving and response curvesRead the physics from each differential-equation term
Simple harmonic motion follows from a linear restoring acceleration and exchanges kinetic with potential energy.
- simple harmonic motion
- phase and energy
- damped oscillator roots
- forced response
- resonance curves
Wave Motion and Superposition
travelling waves, energy transport, interference, standing modes and beatsSeparate motion of the pattern from motion of the medium
A travelling wave carries energy through a medium while particles oscillate locally. Wave number and angular frequency encode wavelength and frequency, and the phase sign fixes direction.
- travelling-wave functions
- wave speed and power
- reflection and transmission
- standing-wave modes
- beats and superposition
Its scope starts with dimensional analysis and vectors, then develops kinematics, Newtonian dynamics, momentum, systems of particles, rotation, angular momentum, work and energy, gravitation, oscillations and waves. The teaching notes emphasise conceptual ideas alongside mathematical treatment, so the useful revision question is never only which formula applies.
You must also say why its assumptions fit the system, which quantity is conserved across the chosen boundary, and what the answer means physically.
How the topics connect
Vectors and calculus provide the language. Newton's laws explain local changes in motion, while impulse and energy integrate those changes over time or position.
Centre-of-mass and rotational methods compress many-particle motion without discarding the effect of mass distribution. Gravitation supplies an inverse-square field in which force and energy methods can be compared.
Oscillations and waves then turn the earlier differential equations into recurring patterns, with damping, driving, resonance and superposition providing the final layer.
How to prepare for assessment
The problem sets use multipart derivations, moving constraints, collisions, extended bodies and coupled translation and rotation.
Prepare by writing diagrams and equations from a blank page, retaining symbolic expressions until the last stage and checking units and limiting cases. The worked examples in this guide are original, but they mirror the reasoning roles visible in the course problems and solutions. The published final is a two-hour written examination, and the mid-term test is also two hours.
One A4 sheet with notes on both sides is permitted in each, so build it from the relations you fail to reconstruct during practice rather than copying the notes at miniature scale.
Worked example · free
Choose the shortest valid method for a rolling descent
- 3Write translational and rotational kinetic energy.
- 3Apply the no-slip relation and solve.
- 2Compare with a sliding particle.
Key terms
- Impulse
- The time integral of force, equal to the change in linear momentum.
- Moment Of Inertia
- The mass-weighted squared distance from a specified rotation axis.
- Angular Momentum
- The rotational momentum measured about a stated origin or axis.
- Centre Of Mass
- The mass-weighted mean position whose translation is controlled by external force.
- Conservative Force
- A force whose work depends only on endpoints and permits a potential energy.
- Restitution
- The ratio of relative separation speed to relative approach speed along impact.
- Static Friction
- A responsive contact force that prevents slipping up to its limiting magnitude.
- Radial Acceleration
- The inward acceleration required to change the direction of velocity on a curved path.
- Critical Damping
- The damping level giving the fastest return to equilibrium without oscillation.
- Resonance
- The enhanced steady response when a driving frequency lies near a natural frequency.
- Standing Wave
- A fixed node-and-antinode pattern formed by equal waves travelling in opposite directions.
- Group Velocity
- The speed at which a wave packet and its energy envelope propagate.
PHYS2250 FAQ
How is the course assessed?
The published split is a final written examination worth half the course, a mid-term test worth one quarter, laboratory works worth fifteen per cent and assignments worth ten per cent. Those numeric shares sum to the full course mark. The current sheet calls the mid-term a two-hour test, while the older teaching-note summary calls it a quiz.
What is known about the final examination?
The course materials state that it is a two-hour written examination worth fifty per cent. They do not publish a section count or question-type breakdown in the captured material. Prepare across the mechanics syllabus and check Moodle for the exact schedule and any later format notice.
What does the current mid-term cover?
The current important-dates sheet states that the mid-term test covers Chapters 1 to 8 and is scheduled for 30 October 2026. Because course coverage can move, use that as the captured position and confirm the live Moodle notice before the test.
Can I take notes into the written tests?
Yes. The course Moodle page states that students may bring one A4-sized sheet with printed or handwritten notes on both sides to the midterm and final exams. Build the sheet around conditions and decision points so that a relation is never separated from the assumption that makes it valid.
How should I study the problem sets?
Attempt each question from a blank diagram before reading the matching solution. After checking the answer, identify the first decision that differed: system boundary, axes, force list, constraint, conservation law or algebra. Then redo the problem with changed numbers or geometry so that recognition cannot substitute for solving.
What makes the course mathematically demanding?
The assumed background includes vectors, differentiation, integration, ordinary differential equations, trigonometry and complex numbers. Difficulty comes from connecting those tools to a physical representation. A clean diagram and declared coordinate system reduce the algebra because they determine signs and constraints before calculation.
How should laboratory work affect revision?
Laboratory work is part of the published assessment and the course requires two in-person sessions. Use it to practise uncertainty, graph interpretation and reporting rather than treating it as separate from mechanics. The laboratory policy also sets attendance, file-format and late-submission consequences, so check the current instructions before each session.
Questions students ask in each PHYS2250 chapter
- Can dimensional analysis prove a formula?
- No. Matching dimensions is necessary but not sufficient, because a dimensionless numerical factor or function may still be wrong. A mismatch does disprove the relation immediately, making the check valuable before detailed algebra and numerical substitution begins. Chapter 01 · Dimensions and Vector Reasoning
- Is acceleration zero at maximum height?
- No. The vertical velocity is momentarily zero, but gravitational acceleration remains downward. Horizontal velocity also remains present when resistance is neglected, so the total velocity is generally nonzero. Chapter 02 · Kinematics and Projectile Motion
- Do action and reaction cancel?
- They act on different bodies, so they never cancel on a one-body free-body diagram. They cancel internally only when both bodies belong to the chosen system and total momentum is considered. Chapter 03 · Newtonian Dynamics and Constraints
- Is static friction always equal to its maximum?
- No. It adjusts to the value required to prevent slip and equals its maximum only at impending motion, where the direction of likely sliding is also identified. Chapter 04 · Circular Motion and Non-inertial Frames
- When is momentum conserved?
- When the net external impulse on the chosen system is zero or negligible over the interval. Internal collision forces then cancel in the total momentum balance for that system. Chapter 05 · Impulse, Momentum and Collisions
- Can the centre of mass lie outside a body?
- Yes. A ring has its centre of mass at an empty geometric centre, and curved bodies may place it outside their material while retaining symmetric mass moments about the relevant axes. Chapter 06 · Systems of Particles and Centre of Mass
- Why can a hinge reaction disappear from torque?
- Its line of action passes through the hinge, giving zero lever arm about that origin. It still appears in the force balance when translational acceleration or support loading is required. Chapter 07 · Rotational Kinematics and Dynamics
- Why state the origin for angular momentum?
- External torque and angular momentum depend on that origin, so conservation may hold about one point but not another during the same physical interaction and time interval. Chapter 08 · Angular Momentum and Rolling Motion
- Is energy lost to friction?
- Mechanical energy decreases, but total energy is transferred into internal energy and surrounding thermal motion. State the system boundary to describe the transfer and identify where the energy appears. Chapter 09 · Work, Energy and Conservative Systems
- Why is gravitational potential negative?
- Zero is chosen at infinite separation. Bringing masses together lowers potential energy below that reference because gravity is attractive and positive work is released during inward motion. Chapter 10 · Gravitation and Orbital Motion
- What distinguishes natural and driving frequency?
- Natural frequency belongs to the unforced system parameters, while driving frequency is imposed by the external periodic force and controls the steady-state response after transients decay. Chapter 11 · Oscillations, Damping and Resonance
- How do I read travelling direction from phase?
- Hold phase constant. The form kx minus ωt travels toward positive x, while kx plus ωt travels toward negative x, independent of the instantaneous displacement sign. Chapter 12 · Wave Motion and Superposition
How to study for the exam
Use a three-column error log. In the first column record the representation that should have been drawn: vector diagram, motion graph, free-body diagram, energy curve or phase plot. In the second name the governing law and why its conditions apply. In the third record the check that would have exposed the error, such as dimensions, sign, limiting behaviour or order of magnitude.
Rework the same reasoning on new numbers within two days. For the written tests, practise complete solutions under a two-hour limit and build the permitted A4 sheet only from repeated retrieval failures. Keep formulae beside their assumptions, moments of inertia beside their axes, and conservation laws beside the boundary condition that earns them.
Finish each session with one mixed problem that crosses chapters, because the course's harder questions combine translation, rotation, constraints and energy rather than announcing one topic at a time.
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