Newton's Laws of Motion

First Law — Law of Inertia

An object at rest stays at rest, and an object in motion stays in motion with the same speed and direction, unless acted upon by an unbalanced force.

• Objects resist changes in motion
• Net force = 0 → constant velocity (or rest)

Second Law — F = ma

The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.

ΣF = ma

| Variable | Symbol | Units | |----------|--------|-------| | Net Force | ΣF | N or lb | | Mass | m | kg or slug | | Acceleration | a | m/s² or ft/s² |

Note: 1 slug = 1 lb·s²/ft. In SI: 1 N = 1 kg·m/s²

Third Law — Action-Reaction

For every action, there is an equal and opposite reaction.

• Forces always occur in pairs
• Action-reaction pairs act on different bodies
• Critical for understanding normal forces and cable tensions

Applications

Free Fall

• Only gravity acts: a = g = 9.81 m/s² (down)
• F = mg

Inclined Plane

• Normal force: N = mg cos θ
• Tangential force: F = mg sin θ

Friction

• f = μN (static friction ≤ μ_s × N)

Example

A 10 kg box is pushed with 50 N force on a surface with μ_k = 0.3. Find acceleration.

N = mg = 10 × 9.81 = 98.1 N
Friction = μ_k × N = 0.3 × 98.1 = 29.4 N
ΣF = 50 - 29.4 = 20.6 N
a = ΣF/m = 20.6/10 = 2.06 m/s²

Summary

Newton's laws are the foundation of all mechanics. Master F = ma with free body diagrams and you can solve virtually any dynamics problem.