Impulsive Rolling and Angular Momentum at Contact
During a brief impulsive interaction, linear and angular impulse relations determine post-impact translation and spin; choosing the contact point as angular-momentum origin can eliminate an unknown contact impulse only when its line passes through that point.
Why this shows up in the exam
Impulse applied to wheels · Balls striking rough floors · Minimum-loss transition into rolling
Learn the idea
A short impulse can establish rolling, with angular momentum often simplest about the contact point. A short impulse can establish rolling, with angular momentum often simplest about the contact point. Start from a clear axis, origin, body, and reference frame; the geometry and constraints then decide which rotational law is safe to use.
🧠 Memory hook: Take moments where the unknown contact impulse has no arm.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- M(v_f-v_i) = J_net — Linear impulse-momentum relation.
- L_C,f-L_C,i = J_angular,C — Angular impulse relation about contact point C.
- v_f = R omega_f — Additional condition only if rolling is established after impulse.
How to approach it
- 1Identify all impulses
- 2Choose a useful angular-momentum origin
- 3Apply post-impact rolling only if stated or dynamically justified
Common slip-ups that cost marks
- •Conserving kinetic energy across an inelastic impulse
- •Conserving angular momentum about an origin with external impulse torque
- •Imposing rolling without evidence
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Masses 1 kg and 3 kg lie at x = 0 and x = 4 m. Find the x-coordinate of their centre of mass.
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Centre of Mass of Discrete Particles
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