Newton's Laws and Free Body Diagrams

First Law (Inertia)

An object remains at rest or moves at constant velocity unless acted upon by a resultant (net) force.

Second Law

$\boxed{F_{\text{net}} = ma}$

The net force on an object equals its mass times its acceleration. Direction of $F_{\text{net}}$ = direction of $a$.

Third Law

When body A exerts a force on body B, body B exerts an equal and opposite force on body A.

Third law pairs:

• Same type of force
• Act on different bodies
• Equal magnitude, opposite direction

Rules:

1. Draw the object as a point or simple shape
2. Draw all forces acting on that object (not forces the object exerts on others)
3. Label each force with name and magnitude if known
4. Arrows show direction; length represents magnitude

Common Forces

• Weight ($W = mg$, downward)
• Normal reaction ($N$, perpendicular to surface)
• Friction ($f$, opposing motion/tendency to move)
• Tension ($T$, along string/rope)
• Air resistance / drag (opposing motion)
• Applied / driving force

An object is in translational equilibrium when $F_{\text{net}} = 0$.

• Static equilibrium: at rest
• Dynamic equilibrium: moving at constant velocity

For equilibrium: sum of forces = 0 in every direction.

For an object on a slope at angle $\theta$:

• Component parallel to slope: $mg\sin\theta$
• Component perpendicular to slope: $mg\cos\theta$
• Normal reaction: $N = mg\cos\theta$

• N1: no net force → constant velocity; N2: $F = ma$; N3: equal and opposite on different bodies
• Free body diagrams show all forces on ONE object
• Equilibrium: $F_{\text{net}} = 0$
• On inclines: resolve into parallel ($mg\sin\theta$) and perpendicular ($mg\cos\theta$)