Dynamics: Newton's Laws of Motion

Introduction

This chapter introduces the fundamental principles of dynamics, focusing on Newton's three laws of motion, the concept of force, and the analysis of forces using free-body diagrams. These concepts form the foundation for understanding how objects move and interact in the physical world.

Force

Definition and Units

• Force is the quantity that describes the mechanical interaction between objects, causing them to accelerate.

• It is a vector quantity, meaning it has both magnitude and direction.

• The SI unit of force is the Newton (N):

• The customary unit of force is the pound-force (lbf):

• Conversion between units of mass:

• Example: The force with which 1 pound mass is attracted to the center of the Earth is 1 lbf:

The Vector Nature of Force

Vector Addition of Forces

• Forces are vectors and must be added using vector rules.

• When two forces are applied perpendicularly (e.g., , ), the resultant force is found using the Pythagorean theorem:

• The resultant force acts along the hypotenuse of the right triangle formed by the component forces.

Contact and Field Forces

Types of Forces

• Contact forces result from physical contact between two objects (e.g., friction, tension, normal force).

• Field forces act between objects that are not in physical contact (e.g., gravitational, electric, magnetic forces).

Four Fundamental Forces

Classification and Properties

• There are four fundamental forces in nature, listed in order of decreasing strength:

Newton's Laws of Motion

Newton's First Law (Law of Inertia)

• An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless acted upon by a net external force.

• Inertia is the tendency of an object to resist changes in its state of motion.

• Mass is a measure of an object's inertia; the greater the mass, the less it accelerates under a given force.

Newton's Second Law

• The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass :

• This law quantifies how forces cause changes in motion.

• Units: , ,

Newton's Third Law

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

• If object 1 exerts a force on object 2, then object 2 exerts a force on object 1 such that:

• These forces are equal in magnitude and opposite in direction.

Weight and the Normal Force

Weight

• Weight is the gravitational force exerted on an object by the Earth:

• Where is the acceleration due to gravity.

Normal Force

• The normal force is the component of contact force perpendicular to the surface.

• On a horizontal surface with no other vertical forces:

• On an inclined plane at angle :

Free-Body Diagrams

Purpose and Construction

• A free-body diagram is a graphical representation used to visualize the forces acting on a single object.

• Steps to construct:

  1. Identify the object of interest.

  2. Draw the object as a point or simple shape.

  3. Draw and label all external forces acting on the object, indicating their directions.

  4. Choose an appropriate coordinate system.

• Only forces acting directly on the object are included.

Summary Table: Key Terms and Definitions

Applications and Examples

• Calculating the net force on an object using vector addition.

• Determining the acceleration of an object given the net force and mass.

• Analyzing forces on objects on inclined planes or suspended by ropes.

• Using free-body diagrams to solve problems involving multiple forces.

Additional info: These notes are based on standard introductory college physics content and expand on the provided slides and glossary for clarity and completeness.