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.
Why this shows up in the exam
Vector acceleration · Time-dependent forces · Finding position from force
Learn the idea
Net external force is dp/dt and equals ma when mass is constant. A force changes velocity component by component, while perpendicular velocity components continue.
🧠 Memory hook: Differentiate momentum; integrate acceleration.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum F_ext = dp/dt — general law
- sum F_ext = m a — constant mass
- Delta v = integral(F/m) dt — time-varying force at constant mass
How to approach it
- 1Resolve the net force
- 2Apply each component equation
- 3Integrate and check units
Common slip-ups that cost marks
- •Mixing vector components
- •Using ma for changing mass
- •Dropping initial conditions
🌟 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
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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.
Impulse and Momentum Change
J = integral F dt = p_f - p_i; signs are essential for rebounds and reversals.