Force and Translational Dynamics

Introduction

Force and Translational Dynamics explore why objects move the way they do. While kinematics only describes motion, dynamics examines the causes behind motion - namely, the forces acting on objects. This topic centers around Newton’s Laws of Motion and introduces fundamental ideas about mass, inertia, net force, and equilibrium.

Force: A push or pull acting on an object in a certain direction. Force is a vector quantity — it has both magnitude and direction. Forces can be broken down into horizontal and vertical components using trigonometric functions (sin and cos).

Mass: Represents an object’s inertia - its resistance to changes in motion. It’s a scalar quantity (no direction). Weight, however, is the force due to gravity acting on that mass: W = m·g.

Net Force: The vector sum of all forces acting on an object. According to Newton’s Second Law, F_net = m·a.

Free Body Diagrams: Simple but powerful tools for analyzing forces. They represent all forces acting on a single object using arrows to show direction and relative magnitude.

Common Forces:
- Normal Force
- Friction
- Air Resistance (usually negligible)
- Tension
- Spring Force

Summary of Key Equations

1. F_net = m·a
2. W = m·g
3. F_s = k·x   (Hooke’s Law — spring force)
4. f_k = μ_k·N   (Kinetic friction)
5. f_s ≤ μ_s·N   (Static friction)
6. ΣF = 0   (Equilibrium condition)

These equations summarize the foundation of Newtonian mechanics — relating forces, mass, and acceleration. Understanding how to apply them to different systems (such as pulleys or inclined planes) is crucial to mastering translational dynamics.

Introduction

Summary of Key Equations

Other Resources