Position and Displacement Vectors (Chapter 2)

Lecture by Jason Brown

• Date: February 1st, 2021
• Duration: 49:53
• Platform: Clemson University Kaltura

Key Concepts

Position Vectors

• Definition: A position vector is a vector that specifies the position of a point in space relative to an origin.
• Notation: Often denoted as r.
• Coordinates: Expressed in the form (x, y, z) in a Cartesian coordinate system.

Displacement Vectors

• Definition: A displacement vector represents a change in position of a point from one location to another.
• Calculation: Displacement = Final Position - Initial Position
• Characteristics: Displacement vectors have both magnitude and direction.

Difference Between Position and Displacement

• Position Vectors indicate location relative to a reference point.
• Displacement Vectors indicate the change in position over a period of time.

Vector Operations

Addition of Vectors

• Rule: Vector addition is commutative. A + B = B + A.
• Method: Vectors are added head-to-tail, and the resultant vector is drawn from the tail of the first vector to the head of the second.

Subtraction of Vectors

• Rule: The subtraction of one vector from another is equivalent to adding a vector in the opposite direction. A - B = A + (-B).
• Visualization: This can be visualized by reversing the direction of the vector being subtracted.

Multiplication by a Scalar

• Definition: Multiplying a vector by a scalar changes the magnitude of the vector but not its direction.
• Result: If a vector A is multiplied by a scalar k, the resulting vector is kA.

Applications

• Vectors are used to model various physical phenomena such as force, velocity, and acceleration.

Summary

• Understanding position and displacement vectors is crucial in physics to describe motion.
• Vector operations are fundamental tools in physics and engineering.

This lecture provides a comprehensive overview of position and displacement vectors, foundational topics in kinematics. The understanding of these vectors and their operations facilitates further learning in the study of motion and dynamics.