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# Chapter 4 Motion in Two or Three Dimensions

## Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the…

## Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an…

## Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, Δv,…

## Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the…

## Projectile Motion

An object thrown in the air follows a parabolic path under the influence of Earth's gravitational force. The motion of such an object is called…

## Projectile Motion: Equations

Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids…

## Projectile Motion: Example

The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to…

## Uniform Circular Motion

Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a…

## Non-uniform Circular Motion

In uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all…

## Relative Velocity in One Dimension

The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object…

## Relative Velocity in Two Dimensions

Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to…

## Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using…

## Visualization of High Speed Liquid Jet Impaction on a Moving Surface

Two apparatuses for examining liquid jet impingement on a high-speed moving surface are described: an air cannon device (for examining surface speeds…

## Preparation and 3D Tracking of Catalytic Swimming Devices

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We report a method to prepare catalytically active Janus colloids that "swim" in fluids and describe how to determine their 3D motion using…

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