Force and Motion I: Newton’s Laws

Introduction to Dynamics

Dynamics is a branch of physics concerned with the study of forces and their effects on the motion of objects. The laws governing dynamics are universal and apply to all physical systems, whether on Earth or in space.

• Definition: Dynamics is the study of the forces that cause objects to move or change their motion.

• Universal Laws: Newton’s laws of motion are foundational to dynamics and are considered universal, meaning they apply to all objects and situations.

• Application: These laws are used to analyze and predict the motion of objects under various force conditions.

Issac Newton’s Monumental Work

Sir Isaac Newton’s work, Philosophiae Naturalis Principia Mathematica, published in 1687, laid the foundation for classical mechanics. Newton proposed scientific laws that remain central to our understanding of motion.

• Historical Context: Newton’s Principia introduced the three laws of motion and the law of universal gravitation.

• Impact: These laws are still used today to describe and predict the motion of objects.

Development of the Force Concept

The concept of force is fundamental in physics. Intuitively, a force is a push or pull that can change the motion of an object. Forces are vector quantities, meaning they have both magnitude and direction.

• Definition: A force is any interaction that, when unopposed, will change the motion of an object.

• Vector Nature: Forces are vectors and must be added using vector addition rules.

• Example: In the overhead view of skaters pushing each other, the total force is the vector sum of individual forces.

Free-Body Diagrams

A free-body diagram is a schematic representation used to visualize the forces acting on a single object or system. It helps in analyzing the net force and predicting the resulting motion.

• Isolated Point: The object is represented as a point, and all external forces acting on it are shown as arrows.

• External Forces: Only forces from outside the system are considered.

• Net External Force: The sum of all external forces determines the acceleration of the object.

Equation for Net External Force:

Types of Forces

Several types of forces commonly appear in dynamics problems:

• Weight: The gravitational force exerted by Earth on an object.

• Normal Force: The support force exerted perpendicular to the surface of contact.

• Tension: The force transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends.

System of Interest

When analyzing forces, it is important to clearly define the system of interest. This allows for accurate identification of external forces and proper construction of free-body diagrams.

• System: The object or group of objects being analyzed.

• External Forces: Only forces acting from outside the system are included in the analysis.

Example: Vector Addition of Forces

Consider three skaters pushing each other. The total force on one skater is the vector sum of the individual forces applied by the other two skaters. The direction and magnitude of the resulting force determine the skater’s acceleration.

• Application: Use vector addition to find the net force and predict the motion.

Summary Table: Types of Forces