Week 7 Study Guide — Momentum, Impulse & Collisions

Directly supported

These topics are explicitly named in the lecture deck and tutorial PDFs:

Topic	Direct source coverage
Linear momentum as a vector	Lecture slide 12 (definition, components, sign convention)
Newton’s 2nd Law in momentum form	Lecture slide 13 (${\vec{F}}_{net}=d\vec{p}/dt$, internal vs external forces)
Conservation of momentum	Slide 14 + worked examples on slides 15–16
Collisions as brief, intense interactions	Slide 18
Impulse, $F$–$t$ area, average force	Slide 20
Elastic / inelastic / totally inelastic classification	Slide 21
2-D collision strategy	Slide 23
Tutorial: rocket impulse, equal-mass collisions, freight cars, crash reconstruction	Tutorial 7 + solutions, Exercises 1–4

You’re expected to be able to:

1. Compute $\vec{p}=m\vec{v}$ and resolve it into components.
2. Apply $\sum {\vec{p}}_i=\sum {\vec{p}}_f$ in 1-D and 2-D.
3. Distinguish elastic from inelastic by checking KE conservation.
4. Use $\vec{J}=\Delta \vec{p}={\vec{F}}_{avg}\Delta t$ to recover forces or impulse durations.
5. Combine momentum with kinematics/work-energy for multi-stage crash problems.

Strongly inferred

The lecture almost certainly covers, in this order:

• The definition of momentum as a vector quantity (slide 12).
• The motivation for writing Newton’s second law in $d\vec{p}/dt$ form, and the cancellation of internal forces between system members.
• A statement of conservation of momentum as the limit “no net external force”.
• One or two worked examples (rain-filling carriage, skydiver from a glider) to drill the idea that “system mass can change but total $\vec{p}$ is still conserved”.
• An introduction to impulse as the area under the force–time curve, with a definition of average force.
• The three collision categories (elastic, inelastic, totally inelastic), distinguished by KE behaviour, with the equal-final-speed problem as the worked illustration.
• A short note on 2-D collisions: conserve each Cartesian component independently.

Possible lecture content (not visible in notes)

May appear in the lecture but isn’t fully captured in the PDFs available:

• The general 1-D elastic-collision velocity formulas ($v_{1f}=\frac{m_1-m_2}{m_1+m_2}{v}_{1i}$ etc.) — useful but not strictly required given the worked-from-conservation approach.
• Centre-of-mass framing: ${\vec{p}}_{total}=M_{total}{\vec{v}}_{CM}$ and “no external force ⇒ CM moves uniformly”.
• Coefficient of restitution as a way of parametrising collisions between fully elastic and fully inelastic.
• Worked 2-D scattering problem (e.g. billiard ball glancing off another).

Gaps requiring official source check

• Whether the exam asks for the general 1-D elastic velocity formulas (and lets you quote them) or expects you to re-derive each time from simultaneous momentum + KE.
• Whether the 2-D collision content is examined or only mentioned in passing.
• Whether oblique 2-D collisions with non-zero impact parameter (or scattering angles) are in scope.

Worked examples

Two notes cover the topic at different depths:

• Cheatsheet — every rule, table, and recipe in one page. Includes the full quiz (mixed difficulty, reshuffles every visit).
• In-depth analysis — why momentum is conserved, why elastic ≠ “stuck”, a full Taylor-style argument for why totally-inelastic collisions are maximum-KE-loss, and a step-by-step exam-style sample.
• Lecture summary — the source-faithful reconstruction listing every slide reference.

Specific worked examples available:

Example	Source	Skill demonstrated
Rain in frictionless carriage	Lecture notes p. 1 / Slide 15	Conservation with changing system mass
Skydiver leaves glider	Lecture notes p. 2 / Slide 16	Conservation with shedding mass
Equal-final-speed elastic 1-D	Lecture notes pp. 3–4 / Slide 22	Simultaneous momentum + KE
Rocket impulse	Tutorial Ex 1	Impulse–momentum theorem
0.2 kg + 0.2 kg, elastic and inelastic	Tutorial Ex 2	Equal-mass collisions
Freight cars couple	Tutorial Ex 3	Totally inelastic + KE loss fraction
Drunk-driver crash	Tutorial Ex 4	Two-stage (collision + friction slide)

Common mistakes

• Forgetting that $\vec{p}$ is a vector and dropping the sign on a rebound.
• Confusing momentum conservation (always — when external $\vec{F}=0$) with KE conservation (elastic only).
• Substituting numbers before picking a sign convention.
• In a totally inelastic collision, forgetting that the final mass is $m_1+m_2$ (not just $m_1$).
• Treating “elastic” as “objects stick together” (that’s totally inelastic).
• Conserving momentum through a friction slide. You can’t — switch to kinematics or work–energy after the collision boundary.
• Unit slips: $km/h\to m/s$ via $÷3.6$.
• 2-D: adding magnitudes of momenta instead of components.

Practice questions

Pick from Tutorial 7. Recommended for a first pass:

• Conservation: Exercise 3 (freight cars) — the cleanest practice in totally-inelastic + KE-loss.
• Impulse: Exercise 1 (rocket) — drill the unit prefix.
• Elastic vs inelastic: Exercise 2 — both cases on the same numbers.
• Two-stage: Exercise 4 (crash) — boundary value at the collision, kinematics after.

The cheatsheet quiz (12+ questions) covers conceptual checkpoints and the full set of worked numbers.

Assessment relevance

• Conservation of momentum and the impulse–momentum theorem are exam staples.
• Multi-stage problems (collision then friction slide) are the standard portfolio-style question.
• Expect at least one elastic-vs-inelastic conceptual question and one fully worked numerical collision.

Confidence report

• Directly supported: Slide numbers, formulas, tutorial answers, worked-example numerics — all match the source PDFs.
• Inferred: Lecture order, framing, and the connection between the four sub-topics (presented here as one unified bookkeeping argument).
• Gap: Any extension content beyond the four tutorial problems and the three lecture-note worked examples.

Source files used

• EGD102-Physics/Lecture7_CTP1.pdf (slides 1, 10–23, 25)
• EGD102-Physics/EGD102 - Lecture7 - Notes.pdf (pp. 1–4, Examples 1–3)
• EGD102-Physics/Tutorial 7.pdf (Exercises 1–4)
• EGD102-Physics/Tutorial 7_Solutions.pdf (Exercises 1–4)
• Textbook reference: Wolfson, R. (2020). Essential University Physics, Vol. 1, 4th Ed. SI, Ch. 9.