Momentum Conservation, Recoil, and Mass Flow
For an isolated system sum p_i = sum p_f; steady exhaust thrust is u_rel |dm/dt| with a consistent sign convention.
Why this shows up in the exam
Recoil · Rocket thrust · Bodies collecting mass
Learn the idea
Total momentum is conserved when external impulse is negligible. Guns, jets, sticking bodies, and rockets redistribute momentum within or across a chosen system.
🧠 Memory hook: Choose the system before conserving momentum.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum p_i = sum p_f — isolated system
- F_thrust = u_rel |dm/dt| — steady mass ejection
- F_ext = d(Mv)/dt - u_rel dM/dt — one-dimensional variable-mass balance
How to approach it
- 1Define system and sign
- 2Check mass crossing
- 3Write one signed balance
Common slip-ups that cost marks
- •Ignoring external impulse
- •Wrong exhaust frame
- •Using constant-mass ma
🌟 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.
A 2 kg block moves on a horizontal rough surface with coefficient of kinetic friction 0.2. A horizontal force of 10 N acts on it. Take g = 10 m/s^2. What is its acceleration?
More from Laws of Motion
Newton's laws of motion
Understand and apply Newton's first, second, and third laws to analyze forces, motion, and interactions in various physical situations.
Circular motion and centripetal force
Analyze the forces involved in uniform and non-uniform circular motion, including centripetal force, tension, and friction.
Friction and its applications
Study the types of friction (static and kinetic), their effects on motion, and how friction interacts with other forces in different scenarios.
Impulse, momentum, and conservation laws
Explore the principles of linear momentum, impulse, and their conservation in collisions and explosions.
Inertia and Inertial Frames
In an inertial frame, sum F_ext = 0 implies a = 0. Earth-fixed frames are approximate when rotational effects are negligible.
Newton’s Second Law in Vector Form
In an inertial frame sum F_ext = dp/dt; for constant mass this becomes m dv/dt = ma.