6.1 — Newton’s laws revisited for applications

Before diving into applications, a compact review of Chapter 5's three laws:

Three laws at a glance

First law (inertia): without a net force, velocity is constant. Second law: \vec F_\text{net} = m\vec a Third law: \vec F_{A\to B} = -\vec F_{B\to A}

5-step problem-solving strategy

Every problem in this chapter can be attacked with these five steps:

1. Pick the object(s) — analyze each object separately
2. Draw a free-body diagram — all forces on the object
3. Choose axes — along motion or the dominant force is usually best
4. Write \vec F_\text{net} = m\vec a in each direction — two or three scalar equations
5. Solve simultaneously — equations may couple across objects

Key points to carry from Chapter 5

1. A third-law pair lives on two different objects. If both forces are on the same object, they're not a third-law pair.

2. Static friction can range from zero to \mu_s N. \mu_s N is the ceiling.

3. Friction always opposes motion (or its tendency). Even on an inclined plane, friction is not always upslope — it depends on which way the object moves.

4. The normal force is always perpendicular to the surface. Its magnitude follows from equilibrium perpendicular to the surface — can be less or more than mg (elevator example).

Preview of Chapter 6

• §6.2: circular motion — which force plays the "centripetal" role? Friction, rope tension, gravity, or normal
• §6.3: circular motion with tangential acceleration — a train speeding up on a curve
• §6.4: rotating frames — fictitious forces (centrifugal, Coriolis)
• §6.5: air resistance — why a skydiver reaches terminal velocity

None of these introduces a new tool — it's still F = ma, but with a sharper look at what makes up the net force.

Preview of §6.2

The most important 2D application: an object on a circular path. Central question: what force keeps it on the circle?

📚 See also: Halliday Vol 1, Ch 6, §6.1.

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