Motion in Two Dimensions

Galileo was the first to realize that a moving body can have several separate motions, which are independent of each other. His thinking provides a foundation for Newton’s treatment of acceleration and force.

A body moving at constant velocity can be described by a sum of velocities in two directions, typically x and y co-ordinates.

The path of a projectile may combine constant speed in the horizontal direction with acceleration due to gravity in the vertical direction. This independence of vertical and horizontal motions is counter-intuitive, and only careful teaching combined with demonstration experiments will convince students.

Motion in Two Dimensions

Motion in Two Dimensions

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Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

Motion in Two Dimensions

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1

Two Dimensions

We have analyzed the motion in one dimension so far, such as the movement of a car in a straight line. We will start to analyze the motion in two dimensions in this chapter. There is nothing difficult in this chapter, since the study of motion in two dimensions is all about reducing two dimensional forces into one.

1. Simple Breakdown of Forces

2. Two Dimensional Forces into One

3. One Dimensional Forces into Two

4. Forces involving Gravity

5. Forces in Three Directions

Lesson 1: Vectors – Fundamentals and Operations

1.            Vectors and Direction

2.            Vector Addition

3.            Resultants

4.            Vector Components

5.            Vector Resolution

6.            Component Method of Vector Addition

7.            Relative Velocity and Riverboat Problems

8.            Independence of Perpendicular Components of Motion

Lesson 2: Projectile Motion

1.            What is a Projectile?

2.            Characteristics of a Projectile’s Trajectory

3.            Describing Projectiles with Numbers

1.            Horizontal and Vertical Components of Velocity

2.            Horizontal and Vertical Components of Displacement

4.            Initial Velocity Components

5.            Horizontally Launched Projectiles – Problem-Solving

6.            Non-Horizontally Launched Projectiles – Problem-Solving

Lesson 3 : Forces in Two Dimensions

1.            Addition of Forces

2.            Resolution of Forces

3.            Equilibrium and Statics

4.            Net Force Problems Revisited

5.            Inclined Planes

6.            Double Trouble (a.k.a. Two Body Problems)

Two dimensional motion

Galileo was the first to realize that a moving body can have several separate motions, which are independent of each other. His thinking provides a foundation for Newton’s treatment of acceleration and force.

A body moving at constant velocity can be described by a sum of velocities in two directions, typically x and y co-ordinates.

The path of a projectile may combine constant speed in the horizontal direction with acceleration due to gravity in the vertical direction. This independence of vertical and horizontal motions is counter-intuitive, and only careful teaching combined with demonstration experiments will convince students.

Accelerations have the same additive properties. They too are vectors that can be added by constructing a parallelogram. Forces too are vectors and obey the same addition rule. In other words: when several forces act on a body, each produces its own effect on motion. One force does not interfere with the motion produced by another force.

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