Twenty minutes or less.

Week 7 — Momentum, Impulse & Collisions. Pick a mode. Start a timer. That's it.

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The shortest path to walking in prepared.

Timer

5:00

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5-minute version

Four sub-topics. One sentence each.

Momentum — $p = m v$ ; it’s a vector, so always set a sign convention.
Conservation — when no net external force acts, $\sum p_{i} = \sum p_{f}$ .
Impulse — $J = Δ p = F_{a v g} Δ t$ (area under $F$ – $t$ curve).
Collision class — elastic conserves KE; totally-inelastic objects share a final velocity (max KE loss).

Open the cheatsheet quiz, do 3 easy questions, close it. You’re prepped.

Time	Action
0–5 min	Skim the cheatsheet tables.
5–10 min	Do one Tutorial 7 exercise from scratch — covering pen, write it out.
10–15 min	Take the cheatsheet quiz. Don’t worry about the score.
15–20 min	Read the “two-stage problem” section in the in-depth note so the crash reconstruction makes sense.

Most students slip on two specific things in this week:

Forgetting that momentum is a vector. If a block rebounds and you’ve written its post-collision momentum as $+ m v$ instead of $- m v$ , you’ll get the wrong mass ratio. Always declare “right is positive” before writing equations.
Conserving momentum through a friction slide. In a two-stage crash problem, momentum is conserved across the collision, then you switch to kinematics for the skid to rest. Don’t try to do both with one equation.

p = m v F_{n e t} = \frac{d p}{d t} \sum p_{i} = \sum p_{f}

J = Δ p = F_{a v g} Δ t [N \cdot s]

Elastic: \frac{1}{2} m_{1} v_{1, i}^{2} + \frac{1}{2} m_{2} v_{2, i}^{2} = \frac{1}{2} m_{1} v_{1, f}^{2} + \frac{1}{2} m_{2} v_{2, f}^{2}

Totally inelastic: m_{1} v_{1, i} + m_{2} v_{2, i} = (m_{1} + m_{2}) v_{f}

Task type	What the setup usually looks like
Impulse	A short burn or strike. Given $F$ and $Δ t$ , find $Δ p$ — or given $Δ p$ and one of them, find the other.
Conservation of momentum (1-D)	Two objects, one or both moving; find the unknown post-collision velocity using $\sum p_{i} = \sum p_{f}$ .
Elastic vs inelastic compare	Same masses and initial speeds; compute $v_{f}$ under both assumptions and the KE lost.
Two-stage crash	A collision followed by a friction slide. Use kinematics ( $v^{2} = u^{2} + 2 a d$ ) to find the post-collision velocity, then back-solve momentum.
Changing-mass system	Rain into a carriage, skydiver out of a glider — system mass changes, but total momentum doesn’t.

Sign-blind algebra. Always declare a positive direction; rebounds carry negative momentum.
Elastic ≠ stuck. Stuck-together is totally inelastic. Elastic means rebound + KE conserved.
Wrong “combined” mass. Totally inelastic final mass is $m_{1} + m_{2}$ ; rain-in-carriage final mass is $5000 + m_{r ain}$ , not $5000$ .
Unit slips. $km/h \to m/s$ via $\div 3.6$ . Don’t be the person who forgets.
Conserving momentum through the friction phase. You can’t — friction is a non-negligible external force then.
Misreading the prefix. $124 mN$ is $0.124 N$ . The rocket-impulse question is a thousand-fold trap.
2-D: never add magnitudes; conserve each component independently.

Try these without notes. Five minutes total.

A $0.45 kg$ football moving at $25 m/s$ is caught and brought to rest in $0.05 s$ . What average force does the catcher’s hands feel?
A $1500 kg$ car moving east at $20 m/s$ collides with a stationary $2500 kg$ truck and they couple. Find the common final velocity, then the fraction of kinetic energy lost.
A skater of mass $60 kg$ moving at $4 m/s$ throws a $2 kg$ stone forward at $10 m/s$ (relative to the ground). What is the skater’s new velocity?

Answers:

Question	Answer
1	$F_{a v g} = Δ p /Δ t = 0.45 (25) /0.05 = 225 N$ (directed opposite to the ball’s motion).
2	$v_{f} = 1500 (20) /4000 = 7.5 m/s$ east. $K E_{i} = 3.00 \times 1 0^{5} J$ , $K E_{f} = 1.125 \times 1 0^{5} J$ ; $62.5%$ KE lost.
3	Before: $60 (4) + 2 (4) = 248 kg \cdot m/s$ (skater+stone moving together). After: $58 v + 2 (10) = 248 \Rightarrow v = 228/58 \approx 3.93 m/s$ . The skater slows slightly.

Read the cheatsheet tables.
One Tutorial 7 exercise done from scratch.
Cheatsheet quiz attempted.
Mini self-test attempted.
Can recite, without notes: “momentum is always conserved when external $F = 0$ ; KE only in elastic.”

That’s it. Close the laptop.